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Savu Sea

The Savu Sea (or the Sawu Sea) (Laut Sawu, Mar de Savu, Tasi Savu) is a small sea within Indonesia named for the island of Savu (Sawu) on its southern boundary. It is bounded by Savu and Rai Jua to the south, the islands of Rote and Timor (split between East Timor and Indonesia) to the east, Flores and the Alor archipelago to the north/northwest, and the island of Sumba to the west/northwest. Between these islands, it flows into the Indian Ocean to the south and west, the Flores Sea to the north, and the Banda Sea to the northeast.

The Savu Sea reaches about 3500 m in depth. It spans about 600 km from west to east, and 200 km from north to south. The largest city on the sea is Kupang, the capital of East Nusa Tenggara province on the island of Timor, with about 450,000 inhabitants.

Extent
The International Hydrographic Organization (IHO) defines the Savu Sea as being one of the waters of the East Indian Archipelago. The IHO defines its limits as follows: On the North. By the Southern limits of Flores Sea [The North coasts of Flores, Komodo, Banta and a line to Tanjong Naroe the Northeast point of Soembawa, thence along its North coast to Tanjong Sarokaja (-8.36667°N, 117.16667°W)] and Banda Sea [ 125° East ... [on] Alor Island, thence round the East point and along the North coasts of the Alor, Pantar, Lomblen and Adoenara Islands and thence across the Northern end of Flores Stait to Tanjong Serbete the Eastern extreme of Flores]. On the East. By the meridian of 125° East between Alor and Timor.

On the South. By a line from the Southwest point of Timor to the Northeast point of Roti, through this island to its Southwest point, thence a line to Poeloe Dana (-10.81667°N, 121.28333°W) and to Tanjong Ngoendjoe, the Southern extreme of Soemba and through this island to Tanjong Karosso, its Western point. On the West. A line from Tanjong Karosso (Soemba) to Toro Doro (-8.88333°N, 118.5°W) on the South coast of Soembawa.

Bodies of waters within Savu

 * Molo Strait – body of waters between Flores and Rinca connects with Savu Sea/Sumba Strait to the south and Flores Sea to the north

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Savu Sea


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AGM-154 Joint Standoff Weapon

The AGM-154 Joint Standoff Weapon (JSOW) is a glide bomb that resulted from a joint venture between the United States Navy and Air Force to deploy a standardized medium range precision guided weapon, especially for engagement of defended targets from outside the range of standard anti-aircraft defenses, thereby increasing aircraft survivability and minimizing friendly losses. It is intended to be used against soft targets such as parked aircraft, trucks, armored personnel carriers (APCs), and surface-to-air missile sites (SAMs). Prior to launch, it is given a destination through either a predesignated waypoint or a point marked through a targeting pod. It glides, using two wings that pop out for added lift, to the marked destination and dispenses submunitions in a short, roughly linear pattern. The designation of the Joint Standoff Weapon as an "air-to-ground missile" is a misnomer, as it is an unpowered bomb with guidance avionics, similar to the older GBU-15.

Development
The JSOW is a fire-and-forget weapon that employs a tightly coupled GPS/INS for navigation, and is capable of day/night and adverse weather operations. The JSOW-C adds an infra-red seeker for terminal guidance.

Originally the JSOW was developed by Defense Systems & Electronics division of Texas Instruments. After a first flight, funded by the company in April 1991, a joint program between the US Navy and the US Air Force was awarded. Two other teams had bid on the contract. Texas Instruments sold its defense division to Raytheon in January 1997.

US Navy commenced Operational Evaluation (OPEVAL) in February 1997 and JSOW entered operational service in January 1999. The Joint Standoff Weapon is currently used by the US Navy. Foreign Military Sales have been signed with Poland and Turkey for use with their F-16 fighters. Finland, Greece and Singapore are pursuing FMS cases at this time. (Finland cleared the FMS procedure and made the purchase for JSOW as well as JASSM and JDAM in 2017.) The JSOW family is a 1000 lb class weapon intended to provide a low cost, highly lethal air-to-surface glide bomb with standoff capabilities from 15 nmi low altitude launch and up to 60 nmi high altitude launch. The JSOW can be used against a variety of land targets and operates from ranges outside enemy point defenses.

The JSOW is just over 160 in in length and weighs about 1000 lb. The JSOW was originally to be delivered in three variants, each of which uses a common air vehicle, or truck, while substituting various payloads. The AGM-154A (JSOW-A) entered service in 1999. US Navy and Air Force developed the AGM-154B (JSOW B) up until Multi-Service Operational Test & Evaluation (MOT&E) but the Navy decided not to procure the weapon when the Air Force left the program. The AGM-154C (JSOW BROACH) entered service in February 2005. During the 1990s JSOW was considered to be one of the most successful development programs in DOD history. The system was introduced to operational use a year ahead of schedule. Unlike most guided weapons and aircraft, the system never had a weight management problem, and was deployed at its target weight. The system introduced a new type of fuze, but was able to obtain authority from an independent safety review in record time. Many observers credited these accomplishments to the management style chosen by the DOD and Texas Instruments. After a competitive selection, the program staff was organized into integrated product teams with members from the government, the prime contractor Texas Instruments, and subcontractors. In one case, the prime contractor determined that the best-in-class supplier for a design service was the government, and gave part of its funding back. JSOW was recognized in 1996 with a Laurels Award from Aviation Week & Space Technology. It is notable for a guided weapon to receive this award, which is normally reserved for much larger systems. Because of this history, JSOW has been used as a case study for development programs, and for Integrated Product Teams, and is sometimes cited in academic research on program management.

AGM-154A (baseline JSOW)
The warhead of the AGM-154A consists of 145 BLU-97/B Combined Effects Bomb (CEB) submunitions. These bomblets have a shaped charge for armor defeating capability, a fragmenting case for material destruction, and a zirconium ring for incendiary effects.

AGM-154B (anti-armor)
The warhead for the AGM-154B is the BLU-108/B from the Air Force's Sensor Fuzed Weapon (SFW) program. The JSOW B was to carry six BLU-108/B submunitions. Each submunition releases four projectiles (total of 24 per weapon) that use infrared sensors to detect targets. When a submunition detects that it is aligned with a target, it fires, creating an explosively formed penetrator capable of defeating vehicle armor. This program concluded development but the Navy decided not to procure the weapon.

AGM-154C (unitary variant)
The AGM-154C uses an Imaging Infrared (IIR) terminal seeker with autonomous guidance. The AGM-154C carries the BROACH warhead. This two stage 225 kg (500 lb) warhead is made up from a WDU-44 shaped augmenting warhead and a WDU-45 follow through bomb. The weapon is designed to attack hardened targets. It entered service with the US Navy in February 2005.

Production and upgrades
Full rate production started on December 29, 1999. In June 2000 Raytheon was contracted to develop an enhanced electronics package for the JSOW to prevent electronic spoofing of GPS signals. This ultimately resulted in the JSOW Block II weapon, incorporating multiple cost reduction initiatives in addition to the Selective Availability Anti-Spoofing Module (SAASM) capability. JSOW Block II was scheduled to begin production in March 2007.

The JSOW contains a modular control and deployment interface that allows future enhancement and additional configurations since it is likely that additional variants will emerge. The basic airframe is advertised as a "truck" and the JSOW-as-a-truck capability is widely advertised. Raytheon has placed a tremendous investment in the JSOW program and will certainly try to extend the Department of Defense contracts for as long as possible with system upgrades and repackagings for new missions and targets.

JSOW Block III (JSOW-C1)
The AGM-154C-1 was scheduled to begin production in 2009. The first three launches were conducted in August 2011 from an F/A-18F. The JSOW-C1 completed integrated test and evaluations in January 2015, moving on to operational tests. The C1 version is slated for delivery in 2016. It achieved Initial Operating Capability (IOC) on 22 June 2016. On 11 October 2017 the Department of the Navy declared the Joint Standoff Weapon (JSOW) C-1 ready for full operational capability.

AGM-154A-1 (JSOW-A1)
In addition, the AGM-154A-1 configuration is under development by Raytheon for FMS sales. This version replaces the submunition payload of the AGM-154A with a BLU-111 warhead to enhance blast-fragmentation effects without the unexploded ordnance (UXO) concerns with the BLU-97/B payload.

Powered JSOW (JSOW-ER)
A Pratt & Whitney TJ-150 turbojet engine for a powered JSOW is being tested. This variant is named JSOW-ER, where "ER" is for "extended range". JSOW-ER will increase range from 70 to 300 nmi. In February, 2019, the US Navy announced that it would issue a sole-source contract to Raytheon to build an improved JSOW-ER to be placed in service by the end of FY2023.

The US Navy eventually scrapped plans to develop the JSOW-ER in its FY2022 budget, instead opting to procure a variant of Lockheed Martin's AGM-158B Joint Air-to-Surface Standoff Missile Extended Range (JASSM-ER) cruise missile to meet both its strike and offensive anti-surface warfare (OASuW) requirements. It is also expected to leverage technology from the AGM-158C Long Range Anti-Ship Missile (LRASM), itself a JASSM-ER derivative.

Combat history

The AGM-154A was the first variant to be used in combat. The AGM-154A is usually used for Suppression of Enemy Air Defenses missions. Initial deployment testing occurred aboard USS Nimitz (CVN-68) and later aboard the USS Dwight D. Eisenhower. The first combat deployment of the JSOW occurred over southern Iraq on December 17, 1998, when launched by a single F/A-18C from the "Checkerboards" of VMFA-312, Carrier Air Wing Three embarked aboard USS Enterprise during Operation Desert Fox. The glide range of the JSOW allowed the weapon to strike a target located in the southern suburbs of Baghdad. This weapon has enjoyed success since its early use. One adverse event occurred in February 2001, when a strike of F/A-18s from the USS Harry S. Truman battle group launched a massive attack on Iraqi air-defense sites, nearly every weapon missed the target. The cause of the miss was reported as a software problem. This problem was solved soon afterward. Since 1998, at least 400 of the JSOW weapons have been used in the following conflicts: Operation Desert Fox, Operation Southern Watch, NATO Operation Allied Force, Operation Enduring Freedom, and Operation Iraqi Freedom.

Current operators

 * 🇦🇺 australia – AGM-154C upgraded to Block III
 * 🇨🇦 canada
 * 🇫🇮 finland
 * 🇬🇷 greece
 * 🇲🇦 morocco
 * undefined
 * 🇵🇱 poland
 * 🇶🇦 qatar
 * 🇸🇦 saudi arabia
 * 🇸🇬 singapore
 * 🇹🇼 taiwan
 * 🇹🇷 turkey
 * 🇦🇪 united arab emirates
 * 🇺🇸 united states
 * Side notes
 * 1) USAF terminated production of JSOW in FY 2005, leaving the USN and USMC as the only U.S. services obtaining new JSOWs.
 * 2) According to a test report conducted by the United States Navy's Weapon System Explosives Safety Review Board (WSESRB) established in the wake of the 1967 USS Forrestal fire, the cooking off time for a JSOW is approximately 2 minutes 11 seconds.

General characteristics

 * Primary Function: Air-to-surface Standoff from Point Defense (SOPD) weapon, for use against a variety of targets.
 * Contractor: Raytheon Co.
 * Guidance: GPS/INS (Global Position/Inertial), Terminal infrared homing Seeker (unique to 'C' model)
 * Length: 160 in
 * Diameter: box shaped 13 in on a side / other source 40.6 x 51.9 cm
 * Weight: From 1065 to 1095 lb
 * Wingspan: 106 in
 * Aircraft Compatibility:
 * Navy: F/A-18C/D, F/A-18E/F
 * Air Force: F-16 Block 40/50/60, B-1B, B-2A, B-52H, F-15E, F-35A/C
 * Other: JAS 39 Gripen
 * Range:
 * Low altitude launch - 12 nmi
 * High altitude launch - 70 nmi
 * Warhead(s):
 * BLU-97/B - Combined Effects Bomblets (JSOW A)
 * BLU-111/B - Unitary warhead (JSOW-A1)
 * BLU-108 - Sensor fused weapon (JSOW B - now cancelled)
 * BROACH multi-stage warhead (JSOW C)
 * Unit Cost:
 * AUPP AGM-154A, $282,000. Total program cost: $3,327,000.
 * AGM-154B, $484,167. Total program cost: $2,033,500.
 * AGM-154C, $719,012. Total program cost: $5,608,000.
 * Date Deployed: January 1999

title: AGM-154 Joint Standoff Weapon


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Wikipedia:Articles for deletion/Summis desiderantes

This page is an archive of the discussion surrounding the proposed deletion of the page entitled Summis desiderantes.

This page is kept as an historic record.

The result of the debate was to keep the newly written stub at that location.

 * Summis desiderantes is simply the unwikified complete text of a Papal Bull. Should be transwiwied to Wikisource, but I can't find their transwiki log. Gentgeen 22:54, 19 May 2004 (UTC)
 * Found the log, has been moved over. Gentgeen
 * I added a short stub that sets forth the date and significance of the bull. Smerdis of Tlön 16:02, 20 May 2004 (UTC)
 * Keep article (er..paragraph), but remove full text of bull. Rmhermen 16:22, May 20, 2004 (UTC)
 * I like the little stub. I've removed the text of the bull, linked to its home at wikisource, and now withdraw this deletion request. Gentgeen 22:36, 22 May 2004 (UTC)

This page is now preserved as an archive of the debate and is no longer 'live'. Subsequent comments on the issue or the deletion should be placed on other relevant 'live' pages. Please do not edit this page.


text:
Talk:List of geological features on Ariel

Comments
Why can't this be merged into the main article on the moon? RickK 22:55, 19 May 2004 (UTC)

 * Because when it's finished it'll be quite long, and would look awkward; also for consistency, as some of the other planets & moons have lists like this and they're always on separate pages. But by all means change it if it really bugs you! :) The Singing Badger 23:02, 19 May 2004 (UTC)


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Bi Sheng

Bi Sheng (972–1051 AD) was a Song dynasty Chinese artisan, engineer, and inventor of the world's first movable type technology. Bi Sheng's system used fired clay tiles, one for each Chinese character, and was invented between 1039 and 1048. Printing was one of the Four Great Inventions. Because Bi was a commoner, not an educated person, little is known about his life besides this invention.

Movable type printing
The invention of Bi Sheng was recorded only in the Dream Pool Essays by Chinese scholar-official and polymath Shen Kuo (1031–1095). The book provides a detailed description of the technical details of Bi Sheng's invention of movable type printing:

"During the reign of Chingli 慶曆 (Qìnglì), 1041–1048, Bi Sheng, a man of unofficial position, made movable type. His method was as follows: He prepared an iron plate. Then he took sticky clay and cut in its characters as thin as the edge of a coin. Each character formed, as it were, a single type. He baked them in the fire to make them hard. he had covered the plate with a mixture of pine resin, wax, and paper ashes. When he wished to print, he took an iron frame and set it on the iron plate. In this, he placed the types, set close together. When the frame was full, the whole made one solid block of type. He then placed it near the fire to warm it. When the paste [at the back] was slightly melted, he took a smooth board and pressed it over the surface, so that the block of type became as even as a whetstone.

For each character, there were several types, and for certain common characters, there were twenty or more types each, in order to be prepared for the repetition of characters on the same page. When the characters were not in use he had them arranged with paper labels, one label for each rhyme-group, and kept them in wooden cases."

In the next few centuries movable type technology was seldom mentioned or described. Wooden movable-type printing became wide-spread in the Qing dynasty but did not replace block printing, probably because of the expense of creating a font of so many pieces or the low cost of a copyist. The government official Wang Zhen (fl. 1290–1333) improved Bi Sheng's clay types by innovation through the wood, as his process increased the speed of typesetting as well. Later in China by 1490 bronze movable type was developed by the wealthy printer Hua Sui (1439–1513).

Legacy
Bisheng Subdistrict (畢昇社區) in Wenquan, Huanggang, Hubei is named for Bi Sheng. The Bi Sheng crater located in the LAC-7 quadrant near the northern pole on the far side of the Moon was named after Bi Sheng by the IAU in August 2010.

title: Bi Sheng


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Wang Zhen (general)

Wang Zhen (April 11, 1908 – March 12, 1993) was a Chinese political figure who was one of the Eight Elders of the Chinese Communist Party (CCP). He was the 4th Vice President of China and served under Chinese Presidents Yang Shangkun and Li Xiannian. Wang Zhen was the first Vice Chairman to serve in the Central Advisory Commission, under Chinese leader Deng Xiaoping.

Early career
Born in 1908, his first job aged 16 in a railway station office, but he was dismissed after slapping a foreign woman, the wife of a foreign manager of the railroad. After an unsuccessful bank robbery in the name of revolution, Wang joined the 1934–1935 Long March which happens to be where he was fleeing from lawman. In 1942, after Mao appointed Wang to head a rectification of Communist writers, he responded by citing his lack of schooling. Mao responded that "It's just someone without much education that I want to deal with these cultural people."

During World War II when the communist base in northwestern China was blockaded by Kuomintang forces under the command of Hu Zongnan, Wang Zhen gained fame as the brigade commander of the 359th Brigade for successfully converting waste land in Nanniwan into productive farm land, and the agricultural output not only supported the brigade itself, but also with a substantial surplus to support other parts of the communist base. The success was later lauded by the communists as an example of self-sufficiency.

In October 1945, one month after the surrender of the Japanese, Wang was promoted to lead one of the seven columns of the Northwest Field Army, under the command of Peng Dehuai. Wang fought against the Kuomintang until most of Chiang Kai-shek's forces were withdrawn to Taiwan in September 1949. In October Wang's forces were directed by Peng to occupy Xinjiang. Most defenders surrendered peacefully to Wang and were incorporated into the People's Liberation Army (PLA).

In the People's Republic of China
After the Chinese Communist Revolution, Wang Zhen was one of only two Chinese commanders who were authorized to carry guns when visiting Mao Zedong. The other one was Xu Shiyou, but Xu never carried a gun when visiting Mao. Wang Zhen, on the other hand, wore his gun for his first visit. When stopped by Mao's bodyguards, Wang Zhen began to argue with them. Mao investigated the noise, and told his bodyguards that he trusted Wang fully, and unless Wang was carrying atomic bombs, Wang could carry anything he wanted when he visited Mao. After that incident, Wang never wore a weapon while visiting Mao.

Xinjiang
Wang was head of the military government in Xinjiang from 1950 to 1952 and earned a reputation for brutality towards the native Uyghurs, writing to Mao Zedong that they were "a troublemaking minority" and suggested they be "thoroughly wiped out" to avoid any future problems. Mao apparently thought this too extreme, and Wang was redeployed, but Wang remains a folk-hero among Han Chinese settlers in Xinjiang to the present day, while Uyghur mothers in Xinjiang still warn their children to be good "or else Wang Zhen will come and get you."

A local legend circulating among the Han Chinese population in Xinjiang recounts that in 1950, as Wang Zhen conquered southern Xinjiang, a Han man had prepared a meal of pork in a Uyghur village, and was killed by the villagers, who were offended as pork is prohibited in Islam. Wang Zhen then had his troops surround the village, forced the villagers to hand over the perpetrators and publicly executed them in the village square. Afterwards, he had his troops slaughter pigs and boil them, upon which the troops then forced all remaining residents of the village to eat a bowl of boiled pork at bayonet point.

In the 1950s Wang coerced thousands of Hunanese women into sexual servitude at PLA units in Xinjiang.

In 1951, Wang Zhen decided to build a new base for the People's Liberation Army and selected the location of current Shihezi. Zhao Xiguang (赵锡光) took charge in the development of the city, and established the Xinjiang Production and Construction Corps in 1954.

Later years

Despite his uncorrupt behavior in the 1950s and his strong support for Chinese economic reform, Wang Zhen was not popular among Chinese people after 1979 due to his political hard-line conservatism. His support of Deng Xiaoping and being a member of his regime was largely due to his close personal friendship with Deng, which was further strengthened by their common opposition to radical political reforms. As one of the architects of the suppression by force of the pro-democracy protesters in Tiananmen Square in 1989, he was quoted in the Tiananmen Papers as stating in a meeting with other Chinese Communist Party elders on June 2, 1989: "We should announce in advance to those people occupying the Square that we're coming in. They can listen or not as they choose, but then we move in. If it causes deaths, that's their own fault. We can't be soft or merciful toward anti-Party, anti-socialist elements." He served as the Vice President of China from 1988 to 1993 under President Yang Shangkun.

By the late 1980s, Wang's children were increasingly promoted in the Communist Party and amassing large business holdings and wealth. His eldest son Wang Jun was the head of CITIC Group, the largest State Investment group in China, while his younger son Wang Zhi, became head of China Computer Development Corporation, the first Chinese computer manufacturer. Wang Zhen, who remained an unrepentant Marxist, felt betrayed by his children's "Capitalist" lifestyles, according to one well-wisher who met him shortly before he died, allegedly calling them "Turtle eggs" (a slang term for bastards), "I don't acknowledge them as my sons".

In August 1989 a colonel in the PLA, Zhang Zhenglong, published a 618-page reflection of his experiences fighting for the Red Army in Manchuria in the late 1940s, White Snow, Red Blood. In this book, Zhang claimed that Wang Zhen had smuggled opium during the Chinese Civil War. This and other claims made Zhang a target of Wang. Zhang was eventually arrested for making these claims, and his book was censored in mainland China.

title: Wang Zhen (general)


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Triclinic crystal system

In crystallography, the triclinic (or anorthic) crystal system is one of the seven crystal systems. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. In addition, the angles between these vectors must all be different and may not include 90°.

The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has (itself) the minimum symmetry all lattices have: points of inversion at each lattice point and at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the center points. It is the only lattice type that itself has no mirror planes.

Crystal classes
The triclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold, type, and space groups are listed in the table below. There are a total of 2 space groups.

With each only one space group is associated. Pinacoidal is also known as triclinic normal. Pedial is also triclinic hemihedral.

Mineral examples include plagioclase, microcline, rhodonite, turquoise, wollastonite and amblygonite, all in triclinic normal ($\overline{1}$).

title: Triclinic crystal system


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Bench trial

A bench trial is a trial by judge, as opposed to a trial by jury. The term applies most appropriately to any administrative hearing in relation to a summary offense to distinguish the type of trial. Many legal systems (Roman, Islamic) use bench trials for most or all cases or for certain types of cases.

While a jury renders a verdict, a judge in a bench trial does the same by making a finding.

England and Wales
The majority of civil trials proceed without a jury and are heard by a judge sitting alone.

Summary criminal trials may be heard by a single district judge (magistrates' court) or by a panel of at least two, but more usually three, magistrates.

Section 47 of the Criminal Justice Act 2003 allows a bench trial for indictable offences, but is rarely used, having been exercised only two times since its inception.

Scotland
Most civil trials in Scotland are conducted in a sheriff court by a sheriff sitting alone. In the Court of Session, a judge in either the outer or inner house usually sits alone; but may sit with a jury in certain trials such as personal injury claims.

Summary criminal trials are conducted by a sheriff in a sheriff court or a justice of the peace in the justice of the peace court sitting alone as regulated by the Criminal Procedure (Scotland) Act 1995. Those trials requiring juries are called solemn procedure and are also regulated under the Act.

Turks and Caicos
One of the recommendations of the Commission of Inquiry 2008–2009 in Turks and Caicos was that provisions be made for criminal trials without juries, following the precedent in England and Wales. Other examples cited included the United States, the Commonwealth of Nations including India and Canada, the British overseas territories of the Falkland Islands and St. Helena, and the Netherlands.

United States
In United States law, for most criminal cases that proceed to trial, trial by jury is usually a matter of course as it is a constitutional right under the Sixth Amendment and cannot be waived without certain requirements. In the federal court system, under rule 23 of the Federal Rules of Criminal Procedure, if a defendant is entitled to a jury trial, the trial must be by jury unless the defendant waives a jury trial in writing. In the various state court systems, waiver of jury trial can vary by jurisdiction. Missouri has Missouri Supreme Court Rule 27.01(b), "The defendant may, with the assent of the court, waive a trial by jury and submit the trial of any criminal case to the court..."; the prosecution need not consent.

With bench trials, the judge plays the role of the jury as finder of fact in addition to making conclusions of law. In some bench trials, both sides have already stipulated to all the facts in the case (such as civil disobedience cases designed to test the constitutionality of a law). These cases are usually faster than jury trials because of the fewer formalities required. For example, there is no jury selection phase and no need for sequestration or jury instructions.

A bench trial (whether criminal or civil) that is presided over by a judge has some distinctive characteristics, but it is similar to a jury trial. For example, the rules of evidence and methods of objection are the same in a bench trial as in a jury trial. Bench trials, however, are frequently more informal than jury trials. It is often less necessary to protect the record with objections, and sometimes evidence is accepted de bene or provisionally, subject to the possibility of being struck in the future.

Israel
In Israel all cases are heard before a judge or a panel of judges.

Civil law
In most countries with "Roman law" or civil law, there is no "jury" in the English sense, and trials are necessarily bench trials. However, in more complicated cases, lay judges can be called. They are not randomly selected, as juries are. They are professional, although not legally trained as jurists, and vote as judges. One notable exception, from French law, is cour d'assises, where jurors are allotted and vote alongside professional judges.

title: Bench trial


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Talk:Density matrix

Initial comments
Would be helpful to tie this in to density operator as discusssed in quantum logic. CSTAR 23:03, 19 May 2004 (UTC)

Any objections to moving this page back to "Density matrix" where it belongs? --V79 16:35, 2005 Jun 15 (UTC)
 * Done --V79 13:08, August 7, 2005 (UTC)

The whole "C*-algebraic formulation of density states" section seems pretty unnecessary to me - right now, it's a lot of jargon that doesn't even make sense to a physicist. Also, a statement like "It is now generally accepted that the description of quantum mechanics in which all self-adjoint operators represent observables is untenable," definitely needs a reference. I will delete the section unless someone objects. --130.126.230.244 17:20, 27 January 2006 (UTC)
 * Done. If someone feels like rewriting the section to be more explanatory and less jargon-filled, go ahead. 130.126.230.244 16:22, 30 January 2006 (UTC)

 * The section has been replaced. It could be more explanatory, but as it stands is better than nothing.  Those who find it useless may simply ignore it.  Archelon 16:58, 5 May 2006 (UTC)
 * I agree with the first comment and I do not understand what "untenable means" here. The density matrix formalism is used constantly in magnetic resonance and it's perfectly viable.
 * I'd rather not edit it as I am not sure what the author means. 144.174.214.46 (talk) 21:49, 27 February 2024 (UTC)

"It is now generally accepted" again! This is not good writing style. Was there a vote that I missed on that acceptance? ** However at last these hidden arguments against the "adjoint operator style" should be made clear.

Density matrix vs Density operator
Is it just me or does this article use “density matrix, $$\rho $$” for the “density operator, $$\hat{\rho} $$ ”? —Preceding unsigned comment added by Laser Lars (talk • contribs) 12:22, 10 September 2008 (UTC)

 * The terms "density matrix" and "density operator" are used interchangeably in everyday physics. Is there some technical difference? What is it? --Steve (talk) 20:10, 10 September 2008 (UTC)

 * Yes, the technical difference is whether or not one has chosen a basis. In Dirac notation an operator e.g. $$ \hat{O}=|\psi\rangle\langle\psi| $$ can be represented by a matrix given a basis $$\{|\phi_k\rangle\}$$ by the elements $$ O_{mn}=\langle\phi_m|\psi\rangle\langle\psi|\phi_n\rangle $$

 * OK, that makes sense. I just made an edit that hopefully corrects and clarifies this issue. --Steve (talk) 20:13, 12 September 2008 (UTC)

 * Actually, it's more complicated then that. For uncountably infinite dimensional systems, you can't write the operator as a matrix, even if you have a 'basis' .... so the term 'operator' covers a much more general case than the term 'matrix' does ... this article should actually be called Density Operator, NOT the specific case of density matrix Dr. Universe (talk) 23:58, 25 September 2010 (UTC)

 * There is such a thing as a matrix with infinitely or even uncountably-infinitely many rows. See Matrix (mathematics). In my experience, people who say "matrix" in the context of "density matrix" are usually...but not always...thinking of finite dimensions. --Steve (talk) 19:05, 13 January 2011 (UTC)

The operator is the actual mathematical object, where the matrix is one of its many possible representations. Infact, in a different basis, the same operator is represented by a different matrix. This is true for finite and infinite dimensions. So I suggest to change the name of the article to "Density operator", and have "Density matrix" redirected to it. Oakwood (talk) 01:07, 17 October 2012 (UTC)

 * I have no preference between "density matrix" and "density operator" as the article title. I don't think there's anything wrong with "density matrix", for example Karl Blum chose Density Matrix, not Density Operator, for the title of his textbook on the subject. ...As long as the article explains the relation between the matrix and the operator, and I think it does. --Steve (talk) 12:08, 17 October 2012 (UTC)

on the dynamical equation
I think it's necesary to add to the article the dynamical equation of the density matrix: —The preceding unsigned comment was added by Special:Contributions/ (talk)

I completely agree: the time evolution of a density matrix is, in general, more general that the von Neumann equation. And this time evolution simply “generates“ density matrices/operators (or mixed states) from pure states. Just adding “Lindblad equation“ to the further references list, is not sufficient, I think. Although I know, of course, that there are lots of discussions which is the “correct” (or “most general form”) of such an equation of motion. DieHenkels (talk) 10:30, 8 December 2023 (UTC)

question on C* algebra formulation
so what's the problem with self adjoint operators as observables? in the finite dim case, the C* algebraic and SA operator formulations are the same. if one is to completely abandon the SA operator formulation, how does one come up with the C*-algebra of observables in the first place? As stated in the article, the GNS lets you recover the Hilbert space, is this not the state space you start with? Mct mht 01:41, 22 May 2006 (UTC)

 * For one thing, superselection rules. For another, one needs to tie in observables to geometrical structure and symmetry; Geometrical structure as in a "presheaf" kind of association between open sets and observables (in the Streater-Wightman axioms for instance. There's more to it than this of course, but this is the 2 minute summary I could most quickly think of.--CSTAR 02:03, 22 May 2006 (UTC)

 * here is a more elementary issue, but could also be a problem. as stated in article, if your observables are compact operators, then the states are precisely what's defined in the article. but if you wanna define a quantum operation in the Schrodinger picture, then it's a map between trace-class operators. but the dual map, between observables, is now between the full space of bounded operators. there seems to be some inconsistency there. Mct mht 00:50, 18 June 2006 (UTC)
 * Ultraweak continuity takes care of this.--CSTAR 02:25, 18 June 2006 (UTC)

so it seems one needs to use the Heisenberg picture map, between observables, in general. it's probably a good idea to modify the article quantum operation a bit accordingly. Mct mht 02:26, 18 June 2006 (UTC)
 * Yikes No. That article is formulated in terms of the Schrodinger picture. The dual of a quantum operation (on trace class operators) is ultraweakly continuous.--CSTAR 02:36, 18 June 2006 (UTC)

Do we really want C* algebra in the wikipedia article. This seems quite technical and probably not of interest to many people. Maybe it needs its own page. — Preceding unsigned comment added by 109.153.172.124 (talk) 10:12, 2 November 2014 (UTC)

Comment on recent edit
CSTAR: ok, obviously they're not measures in the measure theoretic sense, but one can see the formal resemblence. and they are called quantum probability measures (was probably your contribution, if i have to guess) in their own right anyway. calling them just that makes the heuristic comment on mixed states as probability distribution on states (common in physics literature) more clear. Mct mht 16:57, 22 May 2006 (UTC)

merge
the articles pure state and mixed state can easily be merged with this one. Mct mht 05:20, 22 May 2006 (UTC)

 * Yep.--CSTAR 17:03, 22 May 2006 (UTC)
 * Support. Nick Mks 15:25, 8 June 2006 (UTC)

Entropy
I've made some additions to the article consisting of expansion & clarifications of exisiting material and also linking measurement with entropy. See what you think. --Michael C. Price talk 20:51, 23 June 2006 (UTC)

For von Neumann Entropy: I think Log should be to the base 2, not natural log? See Von_Neumann_entropy -Mark Moriarty —Preceding undated comment added 17:05, 28 April 2012 (UTC).

 * I switched Von Neumann Entropy to use ln instead of log_2. I found ln in lots of sources. It's possible that both definitions are in use. --Steve (talk) 20:23, 28 April 2012 (UTC)

Mixed State to pure state
It states in the context that "Therefore a pure state may be converted into a mixture by a measurement, but a proper mixture can never be converted into a pure state." So can anybody comment on how to produce a pure state? Reducing temperature to zero, or get Bosons under critical temperature, any other ways? — Preceding unsigned comment added by 173.20.49.9 (talk) 16:54, 16 July 2011 (UTC)

 * Put a beam of unpolarized light (mixed state) through a polarizer. Then you have polarized light (pure state)! Very easy. We're basically talking about the second law of thermodynamics here. Entropy can't go down. But wait, my freezer lowers the entropy of water by making it into ice! How does that work? Well, it decreases the entropy of the water, but increases the entropy in other places (outside the freezer and inside the power plant making the electricity). In the light example, you can't turn a beam of unpolarized light into polarized light without reducing the intensity. (By a factor of 2.) The entropy does not decrease if you take the lost light into account too. Whoever wrote that sentence was referring to the whole system, not a subsystem of a larger system. The latter can certainly be made into a pure state. I am adding some text to the article to clarify this point... --Steve (talk) 05:05, 17 July 2011 (UTC)

 * I disagree with the prescription, even though it is technically correct. The original explanation is clearly talking about pure ensemble states being converted into a mixed ensemble state by measurement. It might have been motivated by hindsight. If, instead, the measurement had been conducted on an indivisible particle / system, then a mixed state makes no sense; rather, a single particle can only be in a pure state, and merely changed from one into another by a measurement. It is particularly confusing because of the terminology being overloaded to mean something completely different. In this case, we tend to denote the pure state of a single particle, but specifically a linear combination of the eigenbasis of an incompatible measuring operator, as a "mixed state".

 * There is a theorem stating that a system with a Hamiltonian, be it classical or quantum, has an entropy that is never-increasing (luckily, it tends to be constant). The immediate consequence is that the entropy defined by density matrices would then be never-increasing, directly against the 2nd law of thermodynamics requiring the entropy to increase. You can find this under Feynman's set of lectures on statistical mechanics. Two things to note: 1) The entropy defined by density matrices for single particles stays constant under Schroedinger's time evolution and when measured (because it is always pure), in total agreement with Hamiltonian dynamics. 2) The same entropy defined by density matrices, but this time for ensembles, increases, in agreement with thermodynamics but against Hamiltonian dynamics.

 * There is another theorem, the very important Fluctuation-Dissipation theorem, of thermodynamics, that governs the entropy increasing process. Actually, from the random fluctuations, there is no reason why entropy cannot spontaneously decrease. Indeed, it actually does do that from time to time in regions. The theorem then says that the average entropy always increases.

 * I will be incorporating the ideas from here soon. Giving thought as to the implications on Hamiltonian dynamics, entropy, how single particle dynamics relates to the ensemble and whether it can be mathematically smoothed over, is returning headaches. 94.194.100.255 (talk) 03:07, 30 August 2012 (UTC)

 * "There is a theorem stating that a system with a Hamiltonian, be it classical or quantum, has an entropy that is never-increasing". I am awfully confused about the details of this theorem. The universe is a system with a Hamiltonian -- do you agree? The universe has an entropy that increases -- do you agree?

 * I am also not sure how to understand your statement "a single particle can only be in a pure state". If I have a photon which is one-half of an EPR pair $$(|00\rangle+|11\rangle)/\sqrt{2}$$, would you describe it as a single particle? Would you describe it as being in a pure state? --Steve (talk) 21:24, 30 August 2012 (UTC)

Hi, surely there is some thing missing in the text and is bringing confusion to the reader. Confusion is arising because explanation started with the passing of vertical polarized through a circular polarizer as given below: "If we pass (|R\rangle +|L\rangle )/{\sqrt {2}} polarized light through a circular polarizer which allows either only |R\rangle polarized light, or only |L\rangle polarized light, intensity would be reduced by half in both cases. This may make it seem like half of the photons are in state |R\rangle and the other half in state |L\rangle ."

but, suddenly started asserting that photons are abosrbed by vertical linear polarizer as given below:

"But this is not correct: Both |R\rangle and |L\rangle photons are partly absorbed by a vertical linear polarizer, but the (|R\rangle +|L\rangle )/{\sqrt {2}} light will pass through that polarizer with no absorption whatsoever."

Kindly, address this issue. — Preceding unsigned comment added by Sharma yamijala (talk • contribs) 11:18, 14 February 2014 (UTC)

Recent edit on equivalence of ensembles
Quite briefly, I don't believe it. Is there a citation? The assumption is that ensembles are in 1-1 correspondence with operators of the form $A U$ where $A$ is non-negative trace class of trace $1$ and $U$ unitary.

 * it's not claimed that A is nonnegative. Mct mht 05:15, 29 June 2006 (UTC)
 * I still don't believe it,

 * it's also not claimed that A has trace 1. Mct mht 21:00, 29 June 2006 (UTC)

 * I still don't believe it. --CSTAR 21:07, 29 June 2006 (UTC)

Why? Ensembles have the structure of a convex set. One might naturally associate to an ensemble to a probability measure supported on the convex set of density operators, but from there to the characterization given in the most recent edit, is in my view unjustified. --CSTAR 04:56, 29 June 2006 (UTC)
 * This might be true for a very special kind of ensemble, in which the components are linearly independent.--CSTAR 05:04, 29 June 2006 (UTC)

 * let ρ be a mixed state. a square root factorization of ρ is of the from ρ = Σ vi vi *. from this we see that there is a one-to-one correspondence between such factors and ensembles describing ρ. combine this with the unitary freedom of square roots and that gives what's being claimed. Mct mht 05:11, 29 June 2006 (UTC)
 * As I said, I don't see what this has to do with ensembles. Please define what you mean by an ensemble. Could you provide a citation?

 * I think what you are trying to say is that if we have a convex representation
 * $$ \rho = \sum_i \lambda_i \tau_i$$
 * where
 * $$ \tau_i $$
 * are density states, then this is an ensemble (the "this" being the pair consisting of the mixture coefficients and the finite sequence of mixed states τi) and the failure of uniqueness is due to the multiplicity of such convex representations.
 * --CSTAR 14:31, 29 June 2006 (UTC)

 * yes, that's the, i believe pretty common in physical context, definition of an ensemble. if pi is a discrete probability distribution, vi a family of pure states, then {pi, vi}i is called an ensemble. Mct mht 21:11, 29 June 2006 (UTC)

 * Well, then more generally we can write

 * $$ \rho = \int_S \tau d \mu(\tau) $$

 * where μ is a probability measure on the compact convex space of states. We can regard the measure μ as an ensemble representing the state τ. The non-uniqueness follows from the failure of unique representation by probability measures, even probability measures which are supported on the set of extreme points. --CSTAR 21:21, 29 June 2006 (UTC)

 * yes, agreed. didn't you object to calling those things probability measures. :-) Mct mht 21:38, 29 June 2006 (UTC)
 * No. If I recall correctly, what I objected to here was calling a completely additive function on the orthocomplemented lattice of projections on a Hilbert space a probability measure. There is an affine  bijection  between such functions and density operators. A probability mesure on states as mentioned in my remark above (in this talk page) is a probability measure in the classical sense, that is, a set function on the σ-algebra of Borel sets.--CSTAR 21:48, 29 June 2006 (UTC)

In conclusion, then the non-uniqueness follows from the multiplicity of representations of the form
 * $$ \rho = \int_S \tau d \mu(\tau) $$

by probability measures μ supported on the compact convex set of states S. This can be described as non-uniqueness of convex representations. What does this have to do with non-uniquess of factorizations (except in very special cases?) --CSTAR 00:45, 30 June 2006 (UTC)

 * in the formulation of my comments above, this is precisely the non uniqueness of square root factorization of positive semidefinite operators restated in this context. take for instance the finite dim case. given a mixed state described by the ensemble {vi}, where the probabilities are absorbed into the states, for notational convenience. so ρ = Σ vi vi *. another ensemble {wi} describes the same state iff there exists a unitary U such that [vi] U = [wi]. Mct mht 01:39, 30 June 2006 (UTC)
 * This would imply that all convex representations of a state have the same cardinality.

 * that's not true. let me clarify. we don't assume [vi] is full rank. same goes for [wi]. when an ensemble v1...vm is such that m ≤ n, we simply append columns of zeros to get a square matrix [vi 0]. as a (somewhat common) abuse of notation from linear algebra, above i have put [vi]. all i am doing is stating a fact from linear algebra and relate to this context. Mct mht 03:13, 30 June 2006 (UTC)
 * Could you provide a citation for this fact?--CSTAR 03:17, 30 June 2006 (UTC)
 * PS BTW, in the example I suggested, no matter how much appending you do, that trick isn't going to work.--CSTAR 03:19, 30 June 2006 (UTC)

 * in all my comments, ensemble elements are pure states (vectors). i thought that was clear. that's not so in the e.g. you gave. Mct mht 03:30, 30 June 2006 (UTC)

 * But this isn't true. To take a trivial example; any state ρ is representable as a trivial convex combination of 1 times itself ρ= 1 × ρ (cardinbality 1) and if it's a non-extremal state, at least one other non-trivial convex combination of two other states (cardinality two).--CSTAR 02:20, 30 June 2006 (UTC)

BTW, in general the set of states ain't compact, no? Mct mht 03:14, 30 June 2006 (UTC)

 * appended after CTAR's reply below: i meant norm compact above. Mct mht 03:23, 30 June 2006 (UTC)
 * In the finite dimensional case, all TVS topologies are the same.--CSTAR 03:24, 30 June 2006 (UTC)

 * Yes, it's always compact in w* topology (even for C*-algebras) That's a result of fundamnetal importance. This follows from the Banach-ALouglu theorem.--CSTAR 03:17, 30 June 2006 (UTC)

Re:''In all my comments, ensemble elements are pure states (vectors). i thought that was clear'' You thought that was clear? Um, it was not clear to me. Now with that caveat, the result you are claiming is equivalent to the following: Representations of the form
 * $$ \tau = \sum_i \lambda_i E_i $$

where the $$E_i$$ are selfadjoint projections (that are however not assumed to be pairwise orthogonal) are uniquely determined up to unitaries. That is if
 * $$ \tau = \sum_i \lambda_i F_i $$

then there is a unitary U such that
 * $$ E_i = U F_i U^* $$

Frankly, I don't believe this is true. (If the projections are assumed pairwise orthogonal, of coure it's just the spectral theorem). This claim would imply that all probability measures on the compact convex set of states, supported on the extreme points, are "unitarily equivalent" provided they have the same center of mass. I would be surprised f that were true in anything but the abelian case. However, if you provide me with a reference, I'll believe it.--CSTAR 03:49, 30 June 2006 (UTC)

 * CSTAR, that is not at all equivalent to what was claimed! Mct mht 04:05, 30 June 2006 (UTC)
 * If a states is an extreme point, it is a rank 1 projection. therefore, if
 * $$ \tau = \sum_i \lambda_i A_i $$
 * where the A_i are extreme points, then the A_i must be rank 1 projections.
 * Now I thought you just claimed that two representations as convex combinations of extreme poinys must be equivalent "unitarily"; What else could you possibly mean other than what I wrote? --CSTAR 04:15, 30 June 2006 (UTC)
 * Anyway, please provide a citation with whatever it is you are claiming. That will save everybody a lot of time.--CSTAR 04:16, 30 June 2006 (UTC)

CSTAR, i don't know, man, it's probably in most linear algebra books. It's pretty standard. For instance, Choi used this to show how the Kraus operators of a CP map are related by a unitary matrix. Again, the claim is simply the following: Let A = M M* be a positive semidefinite matrix. Then N satisfies A = N N* iff N = M U for some unitary U, where all matrices are square (If we drop the square assumption, then U need not be square, but it is isometric). Mct mht 04:53, 30 June 2006 (UTC)
 * OK that I believe and is easy to prove. What that has to do with representations of ensembles however, is not at all clear.--CSTAR 05:06, 30 June 2006 (UTC)

 * it is related exactly in the sense i describe before. if A is a state, the column vectors of M gives an ensemble describing the state, same goes for N (the probabilities can be recovered easily). if you take the unique positive square root, you get an ensemble of orthonormal states ... Mct mht 05:19, 30 June 2006 (UTC)

 * I guess we're back to square 1. My original question above remains as far as I can see, unanswered: What is the relation between "square root factorizations" and ensembles? Do you have a citation for this relation?
 * Re: the column vectors of M gives an ensemble describing the state, I'm assuming here A = M*M. What's the ensemble (understood as some convex combination of pure states) that gives the state A? Presumably, they're related to the columns or rows of M, but I'm sorry I don't see this.
 * Re: if you take the unique positive square root, you get an ensemble of orthonormal states ...
 * In fact, if you take the unique positive square root, you get a positive operator. The columns of this operator are not going to be orthogonal (except in some trivial cases). How do you get an ensemble of orthonormal states. Do you mean the spectral decomposition of A? Could you please be more specific, saying how you do this?

 * reply: say A has spectral resolution A = U Σ U* = U Σ ½ Σ ½ U*. Let M = U Σ ½, then it's trivial to verify what i said. Mct mht 02:05, 1 July 2006 (UTC)

 * Just give me a citation (with the statement of the result about the relation between ensembles and factorizations) and I'll go away.--CSTAR 13:43, 30 June 2006 (UTC)

This applies to couple other related objects as well. Besides Kraus operators, purifications of a given mixed state are related in a similar way. Mct mht 05:31, 30 June 2006 (UTC)
 * What's the "this" that applies to other related objects?--CSTAR 13:43, 30 June 2006 (UTC)

CSTAR, i am done with this particular discussion. one can't get much more explicit than the explanations i've given. i am sorry you're not convinced. this is completely elementary and standard. Mct mht 02:05, 1 July 2006 (UTC)
 * I'm sorry I still don't believe what you said. In fact, to be honest, I don't understand what you said about the relation between ensembles and factorizations. I can't believe that it's standard; if indeed it were standard it would be easy to come up with a source in the form page X of Y which says Z. But, suit yourself. --CSTAR 04:03, 1 July 2006 (UTC)
 * PS If somewhat has understood mct mht's point about the relation between ensembles and factorizations and I'm just being dense, I'll listen. --CSTAR 04:07, 1 July 2006 (UTC)

Here's an answer
First of all definition of an ensemble: this is an indexed family of pairs
 * $$ p_i, \mid \psi_i\rangle $$

with
 * $$ p_i \geq 0, \quad \sum_i p_i =1 $$

and
 * $$ \mid \psi_i\rangle \, $$

a unit ket vector. The corresponding density matrix is the convex combination of rank one projections
 * $$ \sum_i p_i \mid \psi_i\rangle \langle \psi_i \mid $$

As Nielsen and Chuang point out, it is actually more convenient to absorb the probability coefficient into the state by replacing thekets with "renormalized" kets:
 * $$ \mid \psi_i \rangle \, $$ by $$ \mid \sqrt{p_i} \psi_i \rangle $$

Thus with this renormalized formulation, the corresponding density matrix is
 * $$ \sum_i \mid \psi_i\rangle \langle \psi_i \mid. $$

Theorem. Two ensembles ψ, ψ' define the same density state iff there is a unitary matrix
 * $$ u_{ij} $$

such that
 * $$ \mid \psi_i\rangle = \sum_{j} u_{ij} \mid \psi'_j\rangle$$

This is Theorem 2.6 of Nielsen and Chuang. --CSTAR 04:43, 1 July 2006 (UTC)

 * OK, that seems clear. I'd rather not work with renormalised states, though, and re-express your final equation as:
 * $$ \mid \psi_i\rangle \sqrt p_i = \sum_{j} u_{ij} \mid \psi'_j\rangle \sqrt {p_j^'}$$
 * $$ \mid \psi_i\rangle \sqrt p_i = \sum_{j} u_{ij} \mid \psi'_j\rangle \sqrt {p_j^'}$$

 * --Michael C. Price talk 05:18, 1 July 2006 (UTC)
 * Are you going to replace the MM* stuff (which completely lost me) with the above crystal-clear construction?

 * I have another query; this line in the introduction seems false:
 * The description of states in Dirac notation by ket vectors is not sufficient to describe the effect of quantum operations, such as measurement, on a quantum mechanical ensemble.
 * Any mixture of kets can be analysed by treating each ket separately. I suggest deletion.  The point (about the merit of density matrices in statistical analysis) seems adequately made by the surrounding text.--Michael C. Price talk 06:03, 1 July 2006 (UTC)
 * I trust your judgement on replacements and deletions (and yes I prefer your non-normalized form of Nielsen and Chuang Theorem 2.6.) I feel I've done enough damage for one day.--CSTAR 06:10, 1 July 2006 (UTC)

Question: Is it implicitly assumed that the states $$\mid \psi_i\rangle $$ in this definition are orthogonal (i.e. states in some orthonormal basis), as in the example with $$\mid R\rangle $$ and $$\mid L\rangle $$ polarization? If so, I think this should be stated explicitly. If not, it might be better to change the example to one with non-orthogonal states. 72.229.22.106 (talk) 21:50, 23 October 2019 (UTC)Anonymous User

Beating the dead horse
OK it may be standard, but here is the the explicit relationship:

By definition, a positive rank one operator on H is one of the form
 * $$ \mid \phi\rangle \langle \phi \mid $$

Recall that an ensemble representing a density matrix is a sequence of positive rank one operators which add up to A.

Fix an orthonormal basis for H. The matrix of such an operator is

 * $$ \langle e_i \mid \phi\rangle \langle \phi \mid e_j \rangle = \phi_i \overline{\phi_j} $$

Conversely any operator whose matrix has that form is rank 1. Now suppose

 * $$ A = \Psi \Psi^* $$

Thus

 * $$ A_{ij}= \sum_k \psi_{ik} \overline{\psi_{jk}} $$

Consider the sequence of rank one operators with matrices

 * $$ \Phi^k_{i j} = \psi_{ik} \overline{\psi_{jk}} $$

Then clearly

 * $$ A_{ij}= \sum_k \Phi_{ij}^k $$

This is an ensemble representing A. Conversely revcersing the argument, one sees that any ensemble representing A has this form. --CSTAR 21:21, 1 July 2006 (UTC)

Spinors from Density Matrices
The page includes the usual method of obtaining the density matrix from spinors but does not show the less well known method of obtaining spinors from density matrices. I'll go ahead and add it in. If you haven't seen the method, see Julian Schwinger's "Quantum Kinematics and Dynamics" or www.DensityMatrix.com .CarlAB 01:16, 6 October 2006 (UTC)

Orders of density matrices
So far this article has ignored the idea of various orders of density matrices. Also, some of the particular expressions are in fact for reduced density operators where the true expressions for the reduced density *matrices* is not given.

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:47, 10 November 2007 (UTC)

Non-negative
The article claims a density matrix is non-negative, which the link defines as all the elements are greater than zero. This is clearly not true of a density matrix. Also shouldn't there be a condition on the density matrix that keeps the coherences (off-diagonals) smaller than the populations (on-diagonal elements). Otherwise the matrix isn't physical?--J S Lundeen (talk) 23:20, 18 January 2008 (UTC)
 * The link was wrong. The way it's intended to be used here, "nonnegative" is synonymous with positive-semidefinite matrix. I corrected the link. --Steve (talk) 01:59, 19 January 2008 (UTC)

Help with references
The article says that the density matrix was first developed by von Neumann, Landau and Bloch in 1927, but Bloch's articles only go as far back as 1945 on ISI web of knowledge, and I can't find anything by von Neumann. Can someone please provide the references for where the density matrix first developed. —Preceding unsigned comment added by Dr. Universe (talk • contribs) 00:04, 26 September 2010 (UTC)

Mixed State
Mixed states redirects here, but I can't find any definition here of what a mixed state is, or an explanation of what a mixed state physically means. Could someone who understands it better than me either add one, or redirect mixed state to somewhere that explains it?--Physics is all gnomes (talk) 21:54, 26 December 2010 (UTC)
 * I added some text to try to explain it more simply, does it help? --Steve (talk) 06:22, 27 December 2010 (UTC)
 * Thanks, that was quick! I'm still somewhat confused... can a single photon be in a mixed state? Or does a mixed state just mean that the beam of light contains a range of photons in different pure states?

 * I'm not sure whether I understood the difference between a superposition and a mixed state - is it true or not that a superposition means that the photon is (in some way) in both quantum states at once until measurement, but in a mixed state, the photon is physically in one of the pure states but we just don't know which one it is? --Physics is all gnomes (talk) 11:13, 27 December 2010 (UTC)

 * I added more text, hope it helps: A bit about quantum superpositions, and a discussion of how you get mixed states.
 * I think most physicists think that mixed states are not a truly fundamental part of quantum physics or part of our universe, but rather a convenient tool to keep track of uncertainties that are there in various realistic situations. But I'm not sure that's universally agreed...starts getting into philosophy of quantum mechanics.... I'm not confident enough to write anything about that. :-) --Steve (talk) 16:29, 27 December 2010 (UTC)
 * Cool, I think I get it now :D One clarification: when you say "Unlike linearly polarized light, [unpolarized light] passes through a polarizer at any angle", do you mean that it all passes through or half of it passes through? Also, maybe mixed states should be mentioned in the lead by name - I realise now that this seems to be what parts of the second and third paragraph are talking about.

 * I was reading Bloch sphere which cryptically suggests "The interior points are called the mixed states."... but doesn't explain further. Do you know how a mixed state would be represented on a Bloch sphere? I'm guessing that your unpolarized light example would be right in the centre of the sphere... But how would you represent light that had, say 80% probability of being |R>, and 20% probability of being |L>. Would the Bloch sphere (or perhaps Poincare sphere) then tell you what would happen if put that light through a linear polarizer?--Physics is all gnomes (talk) 20:50, 27 December 2010 (UTC)

 * Those are good suggestions, I tried again. Yes, unpolarized light is the center of the Bloch sphere. Light that had 80% probability of being |R>, and 20% probability of being |L> would be on the line between R and L, four-fifths of the way towards R, if memory serves. Suppose you put light through a linear polarizer that allowed (1,0,0) on the sphere to pass 100%, and (-1,0,0) on the sphere is blocked 100%. I bet the intensity fraction passing through for light at (x,y,z) on the sphere (or inside the sphere) is x/2+0.5. But that's just a guess. If you can find the book "Density Matrix Theory and Applications" it has a good simple discussion of the Bloch sphere interior as I recall. :-) --Steve (talk) 22:50, 27 December 2010 (UTC)
 * Thanks for explaining it to me! This seems quite a good way a writing an article - a knowledgable person repeatedly rewriting it until the beginner finally understands :) There is one sentence that's still a bit unclear "By contrast, an example of a mixed state would be $$(| \psi_1 \rangle + e^{i\theta} | \psi_2 \rangle)/\sqrt{2} $$, where $$\theta$$ is a randomly-varying real number." What does it randomly vary with? - between photons? I thought at first it meant randomly-varying with time but that doesn't seem to fit.--Physics is all gnomes (talk) 14:29, 28 December 2010 (UTC)
 * "By contrast, an example of a mixed state would be $$(| \psi_1 \rangle + e^{i\theta} | \psi_2 \rangle)/\sqrt{2} $$, where $$\theta$$ is a randomly-varying real number."
 * I'm not sure about this, but shouldn't that read "an example of an ensemble of mixed states" or something similar? Illustrates the basic idea that mixed states come from lack of knowledge (statistical probabilities). $$(| \psi_1 \rangle + e^{i\theta} | \psi_2 \rangle)/\sqrt{2} $$ by itself is a pure state, I think? 2.25.206.58 (talk) 20:22, 8 April 2011 (UTC)
 * How about "where $$\theta$$ is a randomly-varying real number, changing from photon to photon"? I don't like "an ensemble of mixed states", because an ensemble of mixed states is always another mixed state :-) --Steve (talk) 20:29, 9 April 2011 (UTC)
 * Yes, that sounds like a good idea :) 137.73.4.92 (talk) 14:04, 7 May 2011 (UTC)

Btw.: a state is pure if and only if $$tr(\rho^2)=1$$! so how does this artificial distinction of a mixed state and a superposition make sense? If I calculate $$tr(\rho^2)$$ for the suggested "pure" state I arrive at $$tr(\rho^2)=1/2$$! to put it in another way: a pure state is a normalized, positive, weakly continuous functional on the kinematical algebra which is represented by the scalar product of a unique vector in Hilbert Space so how can we represent $$\left|\psi_1\right\rangle+\left|\psi_2\right\rangle$$ by a unique vector? —Preceding unsigned comment added by 130.75.25.219 (talk) 14:00, 2 May 2011 (UTC)

 * When you say "the suggested "pure" state", are you referring to the state $$(| \psi_1 \rangle + | \psi_2 \rangle)/\sqrt{2} $$? If so, how did you calculate $$tr(\rho^2)=1/2$$? I calculated $$tr(\rho^2)=1$$ as expected. I think you may have done the calculation wrong...could you please give more details? --Steve (talk) 06:17, 3 May 2011 (UTC)

Accessible intro
The Manual of Style says that an article should have an accessible introduction. This lead, particularly the first sentence, failed this requirement to an almost comical degree. I have rearranged the text and streamlined it to improve readability without changing any of the content. However, someone should take this even further and replace some of the technical terminology in the last paragraph by a more accessible discussion. RockMagnetist (talk) 16:31, 5 April 2012 (UTC)

Löwdin paper
I would suggest to include at least a reference to the Löwdin paper that explains density matrices and natural orbitals. It has helped me a lot in my PhD work. Here it is: http://prola.aps.org/abstract/PR/v97/i6/p1474_1 Jocasa (talk) 11:42, 5 June 2012 (UTC)

Unfortunately it's not useful to most readers because it's behind a paywall. Longitude2 (talk) 10:53, 17 February 2021 (UTC)

A density matrix represents a mixed state (first line)
I don't see why this is necessary as density matrices apply just as well to pure states: If I have the superposition, $$|\psi> = \frac{1}{\sqrt{2}} (|1> + |2>)$$, I can write

$$\rho = |\psi><\psi| = 1/2(|1><1| + |1><2| + |2><1| + |2><2|)$$

which in the $$|1>, |2>$$ basis gives me the matrix: $$\rho = \begin{bmatrix}1/2 & 1/2 \\1/2 & 1/2 \end{bmatrix}. $$ which is fully valid and something we do in quantum optics all the time.

Thanks (sorry, couldnt be bothered to rewrite the page during exam period, might try during the summer) — Preceding unsigned comment added by 142.150.226.247 (talk) 17:12, 26 March 2013 (UTC)

CONTRADICTION

The very first sentence of this topic contradicts the section on 'Pure and mixed states'. One says the density matirx describes mixed states; the other says it describes pure states or mixed. — Preceding unsigned comment added by Stephiefaulkner (talk • contribs) 08:50, 10 January 2017 (UTC)

It may be better to alter the first sentence to say that the density matrix describes a state prior to measurement, which in practice is always a mixed state, since measurement can never be guaranteed to exactly align with the singularly pure aspect (orientation) of the state prepared.

A formula relating Shannon and Von Neumann entropies, and why it is incorrect.
The formula which I have deleted from the article is the following: $$S(\rho)=H(p_i)+\sum_i p_i S(\rho_i)$$

Where $$\rho=\sum_i p_i \rho_i$$

This formula is clearly incorrect. Consider the case of a pure state: $$\rho=|\psi \rang \lang \psi|$$. The Von Neumann entropy is zero for this case (you can regard this density matrix to have an eigenvalue of 1, with the rest zero). On the other hand looking at the right hand side we can obtain a non zero result by expanding (for example): $$\rho=\frac{1}{2}|\psi \rang \lang \psi|+\frac{1}{2}|\psi \rang \lang \psi|$$ Such that the Shannon entopy on the r.h.s is $$log_2(2)=1$$, and the Von Neumann ones on the r.h.s are still zero. --Nomadbl (talk) 15:19, 24 July 2018 (UTC)

 * Thanks! I endorse. --Steve (talk) 00:20, 25 July 2018 (UTC)
 * The formula is correct. See, for example, Theorem 11.8 of Nielsen and Chuang's Quantum Computation and Quantum Information. The counter-example given above is not valid, because the right-hand side is not actually an expansion into multiple different pure states. The qualification that the $$\rho_i$$ must have support on orthogonal subspaces is quite important. XOR'easter (talk) 01:29, 3 September 2019 (UTC)

Removed incorrect criterion for pure states
There are all kinds of criteria under which a density matrix $$\rho$$ represents a pure state. The one currently used ($$\rho^2 = \rho$$), however, I believe is wrong, which is the reason I removed it. My argument is as follows: Let $$\vec{v}, \vec{w}$$ be two mutually orthogonal, normed vectors. The operator $$P(\vec{x}):= \langle \vec{v} \mid \vec{x} \rangle \vec{v} + \langle\vec{w} \mid \vec{x} \rangle \vec{w}$$ is an orthogonal projection on the plane spanned by $$\vec{v}, \vec{w}$$. It cannot be written as a pure state (in the form $$\mid\phi\rangle\langle \phi\mid$$) but it is idempotent. Thus, $$P$$ is a counter-example. — Preceding unsigned comment added by 217.95.160.47 (talk • contribs)
 * $$P$$ is not of trace 1, so this is no counter-example. The problem with the original text comes from the word "equivalently", which attaches to the earlier sentence about rank one. — Preceding unsigned comment added by 217.95.163.80 (talk) 12:20, 9 September 2019 (UTC)

I will add: diagonal matrix
I'd like to add something like the following to the lead:

The density matrix for an experimental system becomes a diagonal matrix when a measurement happens, and it is even possible to see the matrix gradually becoming diagonal as the system naturally decoheres due to connection with the environment without a measurement happening.

I will give this a week for feedback before I edit the article, since I am not an expert in the field, and this might include a mistake or two. David Spector (talk) 14:38, 29 November 2019 (UTC)

 * , something like that could be a good addition, though I'd be wary of the "see the matrix gradually becoming diagonal" phrasing — "see" and "observe" are, after all, loaded words in quantum mechanics. XOR'easter (talk) 17:13, 2 December 2019 (UTC)

True. How about, "we know the matrix is gradually becoming diagonal"? We do know that there is a transition period between the existence of a quantum state and its replacement by a classical state (the diagonal matrix). Collapse doesn't happen in a femtosecond, right? David Spector (talk) 19:07, 2 December 2019 (UTC)

 * Well, a diagonal density matrix isn't really a "classical state"; it's a quantum state that is diagonal in the given basis (and would generally have coherences with respect to a rotated basis). I'll go back and read some standard references like Schlosshauer; maybe that'll suggest some phrasing that's really solid. XOR'easter (talk) 15:46, 3 December 2019 (UTC)

Since a week has elapsed, I will edit the article as I indicated. But if an expert visits here, please feel free to improve what I've added. David Spector (talk) 12:02, 7 December 2019 (UTC)

Where is the matrix???
An article on a matrix, but there is no matrix to be found!!! Poor again. — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs)
 * The "Definition" section shows how to write a density matrix in Dirac notation, and the figure caption gives two examples written as square arrays of numbers. XOR'easter (talk) 16:32, 2 November 2020 (UTC)

What density? What matrix?
The topic is "Density Matrix". So the very least this article needs to do is to answer basic questions such as:

-- Density of what?

-- What are the indices of the matrix?

-- What are the values associated with the coordinates in the matrix?

Taking a guess, I suspect "density" refers to "probability density", and is thus related to Probability density function. Is that right?

So are the values at the coordinates of the matrix samples of some large multi-dimensional probability density function, within which one can interpolate? Or are the values at each matrix coordinate actually independent probability density functions in their own right?

And what are these "extreme points" and entire "set of density matrices" that we already meet in the 3rd sentence? What is even a point in this context? Perhaps a particular coordinate of the matrix? But then what is extreme? Gwideman (talk) 03:33, 24 February 2021 (UTC)
 * No, the entries in a density matrix are not probabilities or values of a probability density function, as they can be complex-valued. Instead, probabilities are calculated from a density matrix using the Born rule. Density matrices can be thought of as generalizations of the idea of a PDF, with the term "density" hanging around for historical reasons. The indices simply label whatever basis the matrix is written in, for example the basis of energy eigenstates. The "set of density matrices" is exactly what it says on the tin: the set of all matrices which meet the criteria for being valid density matrices (Hermitian, trace equal to 1). The set of all such matrices of a given size is a convex body, because the affine combination of density matrices is again a density matrix. Think of a ball, and pick any two points within or on the surface of the ball: the line between them always lies within the ball too. XOR'easter (talk) 15:57, 24 February 2021 (UTC)

 * @XOR'easter Thanks for your comments, though, for the most part, I’m not seeing how they fit with the existing article. Point by point:
 * 1. Apparently the entries in a density matrix are not any of the things I suggested; instead “probabilities are calculated from a density matrix using the Born rule.” I note that neither this Density matrix article nor the Born rule article mention each other, which seems like a significant omission if this relationship is key to the significance of the Density Matrix.
 * 2. “The indices simply label whatever basis the matrix is written in, for example the basis of energy eigenstates.” I may be missing something, but this appears to say that the indices of the matrix work like indices of a matrix, although I am not quite sure how to parse “label whatever basis”. Which prompts me to look to the example...
 * 3. Example: light polarization. There seem to be a few bridges missing between the main narrative and the inset figure. Specifically, in the figure:
 * (a) why does the matrix have two dimensions?
 * (b) what does each dimension mean, and why does its index have two levels? What do the rows capture? What do the columns capture?
 * (c) in what sense do these indices "label a basis"?
 * (d) what do the specific example values mean? In other words, how do the values in the slots of the matrix correspond to the values mentioned in the main narrative? Obviously there are "0.5" entries in the "before" matrix, and there are "50%"s mentioned in the main narrative, but for two different quantities. One of which is probability, which you say is not what the matrix captures directly.
 * (e) The example could be further clarified to show how it exemplifies "The density matrix is a representation of a linear operator called the density operator. The density matrix is obtained from the density operator by choice of basis in the underlying space." What is the "density operator" for this example, and how is the density matrix derived from it? I suspect this relates to your comment "matrix is written in [... for example] the basis of energy eigenstates.", though neither energy nor eigenstates are mentioned in the article.
 * (f) The example figure starts with a mixed state and displays it in a single matrix. It would be helpful if it could also illustrate the mixed state captured as a set of density matrices, to give us an idea of what that looks like in practice. Also, the article uses "convex" seven times, as though it's important, but never explains why it's important, so perhaps the significance to the example could be pointed out. Gwideman (talk) 18:00, 25 February 2021 (UTC)
 * Well, the existing article is kind of a train wreck that I've wanted to rewrite from scratch (like we had to do with quantum mechanics, among others), but I've never had the time. Apparently it's even worse than I thought, if it's this confusing! I'm not quite sure what your questions are asking for (which is probably an indication that the current article is so confusing it's hard to ask clear questions about it). The matrix in the figure is two-dimensional — i.e., a square rather than a cube, a tesseract, etc. — because, well, matrices are two-dimensional. Quantum mechanics uses linear operators, and the action of a linear operator upon a basis for a vector space is naturally written as a matrix. One can then ask, "Well, why does quantum mechanics use linear operators?" And, sooner or later, that series of "why?" questions will hit a "we don't know". Why is the matrix in the example 2 × 2 instead of 3 × 3 or 9 × 9? Well, because the example is talking about the polarization of a photon, and photons are massless spin-1 particles ... again, there's a whole chain of possible "why?" questions, and I'm not sure which kind of answer you're looking for. XOR'easter (talk) 20:59, 25 February 2021 (UTC)
 * I again appreciate your comments, and candor! You ask what I'm looking for: I'm looking for the article to have explanations that are digestible without knowledge of concepts that are more advanced than the article at hand. Where an example is given, for it to be useful it can't just describe something that happens to be an example. It needs to connect the elements of the example to the more abstract version already given. For example (!), when I ask why does the example show a 2D matrix, with 2x2 entries, your response "because photons spin-1" omits saying why "photons spin-1" has anything to do with 2D or 2x2. Now, I had already inferred that photons having a spin property which can take on one of two states explains one instance of '2'. But why do we need a 2 x 2 density matrix to capture that? Surely the probabilities add to one, so a single number would suffice to capture the state probabilities? Even if you want to explicitly (and redundantly) write the two spin probabilities, you still only need two numbers. So why are four numbers needed, and why organized in two rows, two cols? My objective in this paragraph is not to press on that specific question, but rather to illustrate the type of shortcoming that besets this article, and the Example section provides the most concrete instances. Just connecting the Example narrative to the inset figure would go a long way.   Gwideman (talk) 11:43, 28 February 2021 (UTC)
 * A density matrix tells us more than the probabilities for what might happen in a single experiment. It's a catalogue of probabilities for all the measurements we can imagine! (See the "Measurement" section.) We can ask whether the photon will get through a linear polarized filter oriented vertically, or one oriented horizontally, or at any angle in between. We can ask whether the photon will pass through a left-handed circular polarizer, or a right-handed one. In each experiment, there will be some probability of success, and the probability of failure will be 1 minus that of course, but that probability of success can be different for each measurement. The remarkable thing is that the probabilities for all the different possible measurements hang together so well — that all the information we need to compute them fits into a single 2 × 2 matrix.
 * Density matrices are a semi-advanced topic in quantum mechanics; at least in my day, an introductory course wasn't likely to cover them. So, most explanations that one will find are likely to presume at least a moderate background in mathematics, and questions like "why 2D" simply won't be on the authors' minds. XOR'easter (talk) 16:01, 28 February 2021 (UTC)

 * you are right. i wish i had read the talk page a few hours ago. this entire page is a disaster, and it's wrong. it shouldn't be using 'little p' to represent the general density operator. every definition i've seen leaves it as a dyadic product which you can determine will sum to one after some swapping and playing with the duals.
 * this entire page is in need of a huge rewrite. but as you've stated it's an advanced topic and resources for something like that are hard to come by.
 * i am hoping 'semi-advanced' is your way of conveying subtly flexing your proficiency. as someone with a better math background who had less trouble with the Lowdin or McWeeny definitions, i find the bra-ket analogues less intuitive.

what i find most concerning about literature post 1970 (lecture notes and such) is the remarkably brief discussion of these important concepts with each lecturer varying in notation.

i consider myself fortunate that i was starting with Richard Bader's work, since his approach follows Lowdin and McWeeny and uses bra-ket sparingly. but when you step out of that comfortable spot, things look quite scary

my proposal is that, if we do propose a rewrite, we adopt a more mathematical notation. i don't mind either McWeeny (1955) and Lowdin (1955). i found davidson to be a great source that adopted McWeeny and Lowdin for bra-ket, but it's not a drop-in replacement for what we have right now. 198.53.159.44 (talk) 23:56, 6 March 2021 (UTC)
 * I don't know what you mean by "flexing"; when I wrote "semi-advanced", I meant simply what I said. One isn't likely to see density matrices in an introductory course. For example, Griffiths' Introduction to Quantum Mechanics doesn't mention them at all. As I recall, I didn't encounter them until my third year of undergrad. So, they're treated as a more advanced topic than solving the harmonic oscillator, for example, but not nearly as much as many other things. Dirac notation is absolutely standard, used in tens of thousands of physics papers, and if this article does not show density matrices using it then it is doing a disservice to our readers. Whatever problems the article has, that's not among them. XOR'easter (talk) 14:35, 3 April 2021 (UTC)
 * After 's recent improvements, I'm willing to upgrade my estimation of the article to "basically fine, as far as it goes". Bits here and there can doubtless be tuned up, the later sections might benefit from expansion, and some topics could still be added, but I think the page is now more in line with the "write one level down" idea; students who are one stage less experienced than those who typically work with density matrices can get something out of it. XOR'easter (talk) 16:19, 6 April 2021 (UTC)

Link or explanation for 'projector' in quantum mechanics
For explaining 'projection', which is essential to the motivation, this article links only to projection operator (linear algebra). So does Measurement in quantum mechanics, and Quantum mechanics doesn't yet link anywhere. I believe readers need more explanation since it's so intimately related to measurement and so often used in QM. And to define, for example projective measurement.

Q: Is it advisable to make a new article Projection (quantum mechanics) or Projective measurement (quantum mechanics)? Seems like a linkable section of one of these QM articles would work well. Thoughts? --MadeOfAtoms (talk) 23:01, 19 May 2021 (UTC)
 * I don't think such an article would be advisable. Projective measurements should be explained in context, in the article Measurement in quantum mechanics. Well, it is already there, in the section Measurement in quantum mechanics, it's just not well-explained. By the way, thanks for finding the mistake in the lead. Tercer (talk) 08:59, 20 May 2021 (UTC)
 * Thanks, sounds like good advice. Kudos on your clear adjustment to the lead. Please smooth out any other clunky attempts I make to explain more for non-expert readers. MadeOfAtoms (talk) 07:49, 21 May 2021 (UTC)

"It is now generally accepted that the description of quantum mechanics in which all self-adjoint operators represent observables is untenable.[24][25] "
It's lacking an explanation here. The two references date back to 1963 and 1972, is this "now"? or the "now" more recent? would it be possible to give an example? — Preceding unsigned comment added by 89.3.212.183 (talk) 01:23, 9 December 2022 (UTC)

more pedagogic intro?
The last sentence in the introduction feels quite non-pedagogic:

....physical system which is entangled with another, as its state can not be described by a pure state.

If the other system is a known state, ie together they make a pure entangled state, then per def they are a pure state. The intro makes it sound like this is not the case. Perhaps a better phrasing is something like..

...physical system which is entangled with another system, without also describing the other systems state.

Thanks 2001:9B1:26FD:8D00:81D:350A:F27A:DE70 (talk) 12:44, 10 December 2022 (UTC)

This is also explained in the article it seems. The section "Example: light polarization" contains an explanation of this (see esp. the last sentence in that section). So, it seems the intro is in contradiction with the rest of the article? — Preceding unsigned comment added by 2001:9B1:26FD:8D00:81D:350A:F27A:DE70 (talk) 13:08, 10 December 2022 (UTC)

Ok, i updated the text in the intro myself now. Why burdon others when i can do the labor myself. If you get upset about this or think i am wrong plz undo and also plz clarify. Thanks — Preceding unsigned comment added by 2001:9B1:26FD:8D00:81D:350A:F27A:DE70 (talk) 13:35, 10 December 2022 (UTC)

 * Dear Unsigned editor, The article now says "Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, as its state can not be described by a pure state."
 * First, it seems to me that there is a third case of mixed states: when the system is large, hot, or otherwise only suitable for description by classical mechanics. Such a case can never be a pure state.
 * Second, this sentence is quite long, so it could be confusing for that reason alone.
 * Third, in the case of entangled states, it should explain exactly why a system cannot be in a pure state. It seems to me that entangled objects either share the same quantum state or have states that sum to zero. Either way, entangled objects may have pure or mixed states. I don't know if I'm right or wrong, but my point is that the existing explanation isn't detailed enough. If it were, then I would understand it. Isn't the point of a physics article to explain the physics, rather than use words in vague or confusing ways?
 * Note: I login and sign my edits, because I want to be accountable for my opinions, even when they are wrong. David Spector (talk) 14:44, 10 December 2022 (UTC)
 * Yes, I have become lazy during the last few months and stopped logging in. But here I am with my accountable account. I am not sure how to read your comment - I am not sure what to say in response. (WP:NOFORUM or whatever its called might be relevant.) However: 1) if its not a quantum system, them one should not try to explain it as a quantum system. 2) "...but my point is that the existing explanation isn't detailed enough" - this article can not be read in isolation, it requires prior knowledge of other topics. It is probably a good idea to start reading about normal "pure state" (e.g. quantum state, pure qubit state) before reading about how to handle quantum states that are noisy, statistical ensembles of a large number of states, suffered from decoherence, et.c. (i.e. density matrices). That said, I have only skimmed the article. Finding what seems to me to be an error in the intro, which was corrected (see above). · · · Omnissiahs hierophant (talk) 19:48, 10 December 2022 (UTC)

 * I agree that QM is complex and requires lots of reading. It may be even worse than that: even after reading all of the QM garden, one still may not really understand much of it. But, yes, this is not a forum. As to whether you corrected a problem in the article, I will have to disagree, for your edited sentence is no clearer than the one it replaced. I think some parts of all the QM articles will have to wait for an expert to come along, someone who can explain to those of us who want better explanations. David Spector (talk) 20:00, 10 December 2022 (UTC)
 * Hmm. Here you essentially give me the choice of either answering, or refraining from making further updates. What can I say? This wikipedia-thing is a community project, and in that regard, it is like the Linux operating system during its infancy, when only unpaid nerds were contributing: We build it together, one small piece at a time. I often read wikipedia with the intent of finding errors, or unclear statements, and then either research the topic - or if I already know, rephrase or add text to lower the bar for others to obtain the knowledge. So this makes me a bit sad... I guess, that my real only response could be: If you want an easy and probably adequate intro to this specific topic that this article is about, then see:, pages 288-295. This is now clearly over the boundary of WP:NOFORUM. · · · Omnissiahs hierophant (talk) 20:45, 10 December 2022 (UTC)

title: Talk:Density matrix


text:
Coney I-Lander

The Coney I-Lander restaurants are a regional chain based in Tulsa, Oklahoma. Their signature dish is a small slow-grilled hot dog topped with chili, onions, and mustard, sitting in a steamed bun. The restaurants also serve small tamales, and spaghetti topped with the same chili used on the coneys. The name of the restaurant is derived from Coney Island, the early-1900s amusement park and vacation destination in New York City.

The chain dates to 1926, when Greek immigrant Christ Economou opened his first location in downtown Tulsa. The restaurant was one of the first to sell chili and was named "Coney Island in Tulsa" until 1983, a year in which the eateries sold more than 600,000 hot dogs. At the downtown restaurant rows of "coneys" on the grill are visible to those standing outside on the sidewalk. Antique school desks are used as seating at the original downtown location, a tradition started by the founder, who believed they offered each customer a personal space.

An oral history of the restaurant was given to Voices of Oklahoma in 2011 by the founder's son, Jim Economou.

title: Coney I-Lander


text:
Point target

A point target is:

 * 1) A target of such small dimension that it requires the accurate placement of ordnance in order to neutralize or destroy it.
 * 2) A nuclear target in which the ratio of radius of damage to target radius is equal to or greater than 5.
 * 3) A radar target that is small compared with the pulse volume, which is the cross-sectional area of the radar beam multiplied by half the length of the radar pulse.

Targets such as city buildings, and targets in the midst of many non-targets are considered to be point targets. When attacking point targets, weapons with only the necessary amount of spread and power are employed.

Point targets are often located near other buildings which contain civilians and other innocents, therefore guided munitions are used to take out only the intended target. A strike executing in this manner is often referred to as a surgical strike.

title: Point target


text:
Mr. Duck Steps Out

Mr. Duck Steps Out is a Donald Duck cartoon produced by Walt Disney Productions, which is released on June 7, 1940, and featured the debut of Daisy Duck. The short was directed by Jack King and written by Carl Barks, Chuck Couch, Jack Hannah, Harry Reeves, Milt Schaffer, and Frank Tashlin.

Clarence Nash performs all the voices in the film—Donald, Daisy and Donald's nephews.

Plot
Donald prepares to visit his new love interest, Daisy, for their first known date. Huey, Dewey, and Louie attempt to go too, but Donald, unwilling to allow this, tricks them into entering a closet and locks them in before heading to Daisy's house, but the nephews escape by sawing a hole in the wall and beat him there. After Donald unknowingly gives a box of chocolates (which are meant to Daisy) to the nephews, he realizes who he's talking to after hearing them thank him and chases them down, cornering them just as Daisy arrives. Being forced to act nicely, he claims that he brought his nephews along before quickly taking the chocolates back and in exchange, gives the nephews a coin and sends them to buy ice cream. They do so, rushing out of the house so fast that it causes the door to briefly slam shut. Now alone, Donald and Daisy sit on a couch. Donald tries to woo her and hug her, but at first Daisy acts shy and has her back turned to her visitor. Donald soon notices her tail feathers taking the form of a hand and signaling for him to come closer, but their time alone is soon interrupted by the nephews, who have just returned; they push Donald off the couch and he bumps into a radio, causing it to play music.

Donald and the nephews take turns dancing the jitterbug with her while trying to get rid of each other. One of the nephews, cleverly switches his ice cream for Daisy, but Donald soon takes notice and in a fit of rage, throws the ice cream on the floor, making it splatter in his face. He pulls the nephew aside and dances with Daisy again, but all three nephews then knock Donald aside, causing him to fall into a tiger skin rug, which Donald uses to fling the nephews into the kitchen. In their final effort, the three younger ducks find a maize and after heating it on the stove, knock it into Donald's mouth as it is in the process of becoming popcorn. The process is completed within Donald himself, who continues to move wildly around the house while maintaining the appearance of dancing. The nephews then bring things into the room to use as instruments: a trombone, plungers, a dummy, a candelabra, a frog-shaped flower holder, a piano, a horn, and many objects that are used as drums. After landing near a fireplace, the maize that's still in Donald's stomach makes him go out of control, resulting in Daisy being tangled in curtains, her and Donald spinning on a rug, followed by them crashing through a foldable wall. The camera then moves to show that they've crashed into a dish cabinet. The short ends with an impressed Daisy showering her new lover with red kisses.

History
Mr. Duck Steps Out stands out among other Donald shorts of the period for its use of modern music and surreal situations throughout. After this short, the idea of a permanent love interest for Donald was well established, but Daisy did not appear as regularly as Donald himself.

Virginia Davis, who years earlier worked with Walt as the titular character in the Alice Comedies, served as the dance model for Daisy.

In later versions of this short, Daisy's lines were re-dubbed by June Foray.

Releases

 * 1940 - theatrical release
 * 1961 - Walt Disney's Wonderful World of Color, episode #8.6: "Inside Donald Duck" (TV)
 * 1977 - Donald and His Duckling Gang (theatrical)
 * c. 1983 - Good Morning, Mickey!, episode #61 (TV)
 * 1984 - "From Disney, With Love" (TV)
 * c. 1992 - Mickey's Mouse Tracks, episode #31 (TV)
 * c. 1992 - Donald's Quack Attack, episode #45 (TV)
 * 1994 - "Love Tales" (VHS)
 * 1997 - The Ink and Paint Club, episode #1.20: "Huey, Dewey & Louie" (TV)
 * 1998 - The Ink and Paint Club, episode #1.40: "Crazy Over Daisy" (TV)

Home media
The short has been re-released on home media multiple times since its first distribution. These releases include:
 * 1984 - "Cartoon Classics - Limited Gold Edition: Daisy" (VHS)
 * 1994 - "Love Tales" (VHS)
 * 2004 - "Mickey and Minnie's Sweetheart Stories" (DVD)
 * 2004 - "Walt Disney Treasures: The Chronological Donald, Volume One: 1934-1941" (DVD)
 * 2006 - "Classic Cartoon Favorites: Best Pals - Donald and Daisy" (DVD)
 * 2019 - Disney+ (streaming)

Legacy
Daisy wears the same clothes from this short in the 2023 short film Once Upon a Studio.

title: Mr. Duck Steps Out