hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Peres–Horodecki criterion
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix  of two quantum mechanical systems  and , to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply. The theorem was discovered in 1996 by Asher Peres and the Horodecki family (Michał, Paweł, and Ryszard)

In higher dimensions, the test is inconclusive, and one should supplement it with more advanced tests, such as those based on entanglement witnesses.

Quantum state
In quantum physics, a quantum state is a mathematical entity that represents a physical system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system.

Quantum states are either pure or mixed, and have several possible representations. Pure quantum states are commonly represented as a vector in a Hilbert space. Mixed states are statistical mixtures of pure states and cannot be represented as vectors on that Hilbert space, and instead are commonly represented as density matrices.

Common examples of quantum states are the wave functions describing position and momentum, finite-dimensional vectors describing spin such as the singlet, and states describing many-body quantum systems in a Fock space.
Steve Spiro
Steve Spiro is a British musician. He started his musical career as a record producer and remixer, working with artists including the Pet Shop Boys, Talk Talk, The Farm and Imagination. Spiro then went on to work with Paul McCartney's keyboard player Paul Wickens, together they created the BBC theme tune for the Atlanta Olympics in 1996, which was picked up by EMI and went on to be a UK hit. They also scored the music for the clay-motion feature Hamilton Mattress, produced by the makers of Wallace and Gromit .

Spiro has also written music for many high-profile television adverts and programs including Sex and the City and Six Feet Under.

In 2011, Spiro released an album of original electronica/dance music entitled Frequent Traveller. It contained thirteen tracks, twelve of which were named after the railway stations on the Victoria to East Grinstead railway line in South London.

Six Feet Under (TV series)
Six Feet Under is an American drama television series created and produced by Alan Ball for the television network HBO. It premiered on June 3, 2001, and ended on August 21, 2005, after five seasons consisting of 63 episodes.

The show follows the Fisher family, who run a funeral home in Los Angeles, along with their friends and lovers. It stars Peter Krause, Michael C. Hall, Frances Conroy, Lauren Ambrose, Freddy Rodriguez, Mathew St. Patrick, and Rachel Griffiths. It was produced by Actual Size Films and the Greenblatt/Janollari Studio, and was shot on location in Los Angeles and in Hollywood studios.

Six Feet Under received acclaim, particularly for its writing and acting, and drew high ratings. It is regarded as one of the greatest television series of all time. The series finale, "Everyone's Waiting", has also been described as one of the greatest in television. Its awards include nine Emmy Awards, three Actor Awards, three Golden Globe Awards and a Peabody Award.
Sanmon Gosan no Kiri
Sanmon Gosan no Kiri (樓門五山桐), or The Golden Gate and the Paulownia Crest, is a kabuki play written by Namiki Gohei I and first performed in 1778.

Originally part of an all-day, five-act jidaimono play called Kinmon Gosan no Kiri ("The Golden Gate and the Paulownia Crest"), only the "Sanmon" scene is currently performed. It is also the only part translated into English.

Unlike many other plays from the Edo period, often adapted from bunraku or noh, Sanmon Gosan no Kiri was written directly for kabuki. It was premiered by the Ōgawa Kichitarō I troupe at the Kado no Shibai theater in Osaka, in the fourth month of 1778. The original cast included Arashi Hinasuke I in the role of Goemon, and Onoe Kikugorô I in the role of Hisayoshi (the kabuki alias for the famous daimyō Toyotomi Hideyoshi).

Jidaimono
Jidaimono (時代物) are Japanese kabuki or jōruri plays that feature historical plots and characters, often famous samurai battles. These are in contrast to sewamono (世話物), contemporary plays, which generally focus on commoners and domestic issues. 'Jidaimono' is usually translated as "period plays". Film and television productions in this mode are called jidaigeki (時代劇), and share many of the same features.
Oka Laila Kosam (soundtrack)
Oka Laila Kosam is the soundtrack album composed by Anup Rubens for the 2014 Telugu-language romantic comedy film of the same name starring Naga Chaitanya and Pooja Hegde in lead roles, directed by Vijay Kumar Konda. The film marks Rubens' second collaboration with Vijay aKumar Konda after Gunde Jaari Gallanthayyinde (2013) and third collaboration with Chaitanya after Manam (2014) and Autonagar Surya (2014). The album consists of six songs with Vanamali, Phani Chandra, Sri Mani, Dasari Narayana Rao, and Anantha Sriram penning the lyrics. The soundtrack album released digitally on 
31 July 2014 on the Aditya Music label. The album received positive reviews from critics.

Oka Laila Kosam
Oka Laila Kosam (transl. For one girl) is a 2014 Indian Telugu-language romantic comedy film written and directed by Vijay Kumar Konda. Produced by Nagarjuna on his home banner Annapurna Studios, the film features Naga Chaitanya and Pooja Hegde. Anoop Rubens composed the music for this film while I. Andrew and Praveen Pudi handled the cinematography and editing departments respectively. This film marked the Telugu debut of Pooja Hegde.

Oka Laila Kosam was released worldwide on 17 October 2014 to positive reviews from critics. Despite the collections being affected due to Cyclone Hudhud, the film was a commercial success at the box office.
Herbert H. Shaw
Herbert H. Shaw (February 16, 1930–c. January 2016) was an American maintenance worker, political gadfly, anti-corruption activist, and prominent perennial candidate from Hudson County, New Jersey who ran for elected office more than 75 times over five decades under the "Politicians Are Crooks" banner.

Henry Helstoski
Henry Helstoski (March 21, 1924 – December 16, 1999) was an American politician and veteran of World War II. Helstoski, a Democrat, represented New Jersey in the United States House of Representatives for twelve years, lasting from 1965 until 1977. He was the representative for New Jersey's 8th congressional district.

He is best remembered for being indicted on charges of receiving bribes from illegal aliens in 1976, but he was never tried as all his charges were dropped by the United States Supreme Court.
Walnut Grove (Tar Heel, North Carolina)
Walnut Grove, also known as Robeson Plantation, is a historic plantation house complex and national historic district located near Tar Heel, Bladen County, North Carolina.  The house was built about 1855, and is a two-story, frame house, five bays wide and four bays deep, in the Greek Revival style.  The front and rear facades feature three bay double porches.  Also on the property are the contributing dining dependency, kitchen, dairy, smokehouse, barn, well, cold frame, and scalding vat.

It was added to the National Register of Historic Places in 1975.

Plantation house
A plantation house is the main house of a plantation, often a substantial farmhouse, which often serves as a symbol for the plantation as a whole. Plantation houses in the Southern United States and in other areas are known as quite grand and expensive architectural works today, though most were more utilitarian, working farmhouses.
Waitin' for the Deal to Go Down
"Waitin' for the Deal to Go Down" is a song written by Charlie Black, Bobby Fischer, and Austin Roberts. It was first recorded by Reba McEntire on her 1990 album Rumor Has It.

It was later the debut single for American country music group Dixiana.  It was released in February 1992 as the first single from the album Dixiana.  The song reached #39 on the Billboard Hot Country Singles & Tracks chart.

Austin Roberts (singer)
Austin Roberts (born George Austin Robertson Jr.; September 19, 1945 – November 1, 2024) was an American singer and songwriter. His most successful recording was 1975's "Rocky"; a transatlantic top 40 hit single. He also wrote several songs that featured in episodes of Scooby-Doo Where Are You! and performed the theme for season 2 of the show.
Pharyngeal branches of glossopharyngeal nerve
The pharyngeal branches of the glossopharyngeal nerve are three or four filaments which unite, opposite the constrictor pharyngis medius, with the pharyngeal branches of the vagus and sympathetic, to form the pharyngeal plexus.

Branches from this plexus perforate the muscular coat of the pharynx and supply its muscles and mucous membrane.

Middle pharyngeal constrictor muscle
The middle pharyngeal constrictor is a fan-shaped muscle located in the neck. It is one of three pharyngeal constrictor muscles. It is smaller than the inferior pharyngeal constrictor muscle.

The middle pharyngeal constrictor originates from the greater cornu and lesser cornu of the hyoid bone, and the stylohyoid ligament. It inserts onto the pharyngeal raphe. It is innervated by a branch of the vagus nerve through the pharyngeal plexus. It acts to propel a bolus downwards along the pharynx towards the esophagus, facilitating swallowing.
2024 Bad Waltersdorf Trophy – Doubles
Constantin Frantzen and Hendrik Jebens were the defending champions but chose not to defend their title.

Petr Nouza and Patrik Rikl won the title after defeating Guido Andreozzi and Sriram Balaji  6–4, 4–6, [10–5] in the final.

Patrik Rikl
Patrik Rikl (born 6 January 1999) is a Czech tennis player who specializes in doubles. He has a career-high doubles ranking of No. 43 achieved on 9 February 2026 and a singles ranking of No. 392 achieved on 1 October 2018. Rikl has won two ATP Tour and five ATP Challenger doubles titles.
Railway Accident Investigation Unit
The Railway Accident Investigation Unit (RAIU) investigates accidents and incidents on Irish railways. It is an independent investigative agency of the Government of Ireland, housed within the Department of Transport. The RAIU's head office is in Dublin.

The RAIU's investigations are carried out in accordance with the Railway Safety Act 2005, the Railway Safety Directive 2004/49/EC and Statutory Instrument No. 258 of 2014 European Union (Railway Safety) (Reporting and investigation of serious accidents, accidents and incidents) Regulations 2014.

Department of Transport (Ireland)
The Department of Transport (Irish: An Roinn Iompair) is a department of the Government of Ireland that is responsible for transport policy and overseeing transport services and infrastructure. The department is led by the Minister for Transport.
Elias Atallah
Elias G. Atallah (Arabic: إلياس  عطا الله; born 1947), is a Lebanese politician and an elected member of parliament during the 2005 elections. He is also the chairperson of the Democratic Left Movement, and a prominent member in the March 14 Alliance. He was born in the Chouf region and has a degree in psychology and philosophy from the Lebanese University.

2005 Lebanese general election
General elections were held in Lebanon in May and June 2005 to elect the 128 members of the Parliament of Lebanon. They were the first elections in thirty years without a Syrian military or intelligence presence in Lebanon. These elections were the first in Lebanese history to be won outright by a single electoral block and were also the first to be monitored by the United Nations.
Serghei Gafina
Serghei Gafina (born 10 November 1984) is a Moldovan footballer who plays as a defender for Dinamo-Auto Tiraspol in the Moldovan National Division. He has previously played for Iskra-Stal Rîbnița, Zimbru Chișinău and Iskra Rîbnița.

Moldovan Liga
The Moldovan Liga, officially known as Liga 7777 for sponsorship reasons, is an association football league that is the top division of Moldovan football league system. The competition was established in 1992, when Moldova became independent from the Soviet Union. It was formed in place of former Soviet republican competitions that existed since 1945. Before the Soviet occupation of Bessarabia and Northern Bukovina in 1940, clubs from modern Moldova competed in the Romanian football competitions.

There are currently eight teams in the competition. At the end of the season, the bottom club is relegated to Liga 1 and replaced by the lower league's champion.

Sheriff Tiraspol – located in Transnistria – is the most successful league club with 21 titles, followed by Zimbru Chișinău with eight wins and Milsami Orhei with two wins. Constructorul Chișinău, Dacia Chișinău and Petrocub Hîncești also won the title on one occasion each.
Nandyal Assembly constituency
Nandyal Assembly constituency is a constituency in Nandyal district of Andhra Pradesh that elects represtatives to the Andhra Pradesh Legislative Assembly in India. It is one of the seven assembly segments of Nandyal Lok Sabha constituency.

N. M. D. Farooq is the  MLA of the constituency, having won the 2024 Andhra Pradesh Legislative Assembly election from Telugu Desam Party. As of 2019, there are a total of 256,573 electors in the constituency. The constituency was established in 1951, as per the Delimitation Orders (1951).

Telugu Desam Party
The Telugu Desam Party (abbr. TDP; transl. Party of the Telugu Land) is an Indian regional political party primarily active in the states of Andhra Pradesh and Telangana. It was founded by Telugu matinée idol N. T. Rama Rao (NTR) on 29 March 1982 and has focused on supporting Telugu people. The party has won a five-time majority in the Andhra Pradesh Legislative Assembly and has emerged as the most successful political outfit in the state's history. It is currently the ruling party in the Andhra Pradesh Legislative Assembly.

From 1 September 1995, the TDP was led by N. T. Rama Rao's son-in-law, Nara Chandra Babu Naidu as the national president of the party. The headquarters of the party is called N. T. R. Bhavan, which is located at Mangalagiri, Andhra Pradesh.
Bob Hay (general)
Major General Robert Arthur Hay, CB, MBE (9 April 1920 – 28 January 1998) was an Australian Army general. He also played Australian rules football and made two appearances in 1942 for Richmond in the Victorian Football League (VFL).

Both of Hay's VFL games were finals. He made his debut in Richmond's semi-final win over Essendon at Princes Park and also played in the 1942 VFL Grand Final two weeks later against the same opponent, as a half forward flanker. Richmond lost the grand final by 53 points and Hay never played again for the club.

Hay went on to have a distinguished career in the Australian Army, serving as Commander of Australian Military Forces in Vietnam from 1969 to 1970. He was Commandant of the Royal Military College in Duntroon.

1942 VFL grand final
The 1942 VFL Grand Final was an Australian rules football game contested between the Essendon Football Club and Richmond Football Club, held at the Princes Park in Melbourne on 19 September 1942. It was the 44th annual Grand Final of the Victorian Football League, staged to determine the premiers for the 1942 VFL season. The match, attended by 49,000 spectators, was won by Essendon by a margin of 53 points, marking that club's seventh premiership victory and first since 1924.
Black–orange coalition
The Black-orange coalition (German: Schwarz-orange Koalition) in German politics refers to a coalition between the centre-right CDU/CSU and the Free Voters (FW). The coalition has only been active in Bavaria since 2018, in both the Second Söder cabinet and Third Söder cabinet. The coalition has also been described as the Bavaria Coalition, Spezi Coalition and Papaya Coalition. In Austria, the black-orange coalition could refer to a coalition of the Austrian People's Party and the Alliance for the Future of Austria.

Second Söder cabinet
The Second Söder cabinet was the state government of Bavaria from November 2018 to late 2023. It was sworn in on 12 November 2018, after Markus Söder was elected as Minister-President of Bavaria by the members of the Landtag of Bavaria. It was the 27th Cabinet of Bavaria.

It was formed after the 2018 Bavarian state election, by the Christian Social Union (CSU) and Free Voters (FW). Excluding the Minister-President, the cabinet comprised fourteen ministers and three state secretaries. Eleven ministers and two state secretaries were members of the CSU and three ministers and one state secretary were members of the Free Voters.
Auvézère
The Auvézère (French pronunciation: [ovezɛʁ]; Occitan dialect: Auvesera) is a 112 km long river in the Nouvelle-Aquitaine region of France. It is a tributary of the river Isle, which is itself a tributary of the Dordogne.

Le Change
Le Change (French pronunciation: [lə ʃɑ̃ʒ]; Limousin: Lo Chamnhe) is a former commune in the Dordogne department in Nouvelle-Aquitaine in southwestern France. On 1 January 2017, it was merged into the new commune Bassillac et Auberoche.
Monument to the Fallen, Pistoia
The Monument to the Fallen (Italian: Monumento ai Caduti) is a Fascist-era monument located in the center of Piazza San Francesco in Pistoia, Tuscany, Italy. The monument was meant to recall those fallen in the battles of World War I between 1915 and 1918. Though completed some years before, the bronze statue was only installed in 1926 with the King in attendance. The bronze statue shows a muscular, partly nude, semi-recumbent man sheltering a statue of Victory as he glares to the distance. The statue is on a marble base with flanking bas-reliefs depicting a winged victory and a mother and child sharing bundles of wheat (fasces). The sculptor, Silvio Canevari (1891–1953), would go on to sculpt statues of athletes for the Stadio dei Marmi in Rome. Many of this statues, including The Pugilist and his Monument to Victory (commemorating those who fell in the wars of Africa) at Civita Castellana, also focus on the athletic man in combat.

Victoria (mythology)
In ancient Roman religion Victoria was the deified personification of victory. She first appeared during the first Punic War, seemingly as a Romanised re-naming of Nike, the goddess of victory associated with Rome's Greek allies in the Greek mainland and in Magna Graecia. Thereafter she comes to symbolise Rome's eventual hegemony and right to rule. She is a deified abstraction, entitled to a cult. But unlike Nike, she has virtually no mythology of her own.
2020–21 Armenian Cup
The 2020–21 Armenian Cup was the 30th edition of the football competition in Armenia. The competition began on 18 September 2020 and ended on 15 May 2021. The winners of the competition earned a place in the first qualifying round of the 2021–22 UEFA Europa Conference League.

Noah were the defending champions of the cup after defeating Ararat-Armenia in the previous season's final on penalties.

Gandzasar Kapan announced that they were withdrawing from the Armenian Cup due to financial difficulties related to the COVID-19 pandemic in Armenia and the 2020 Nagorno-Karabakh conflict.

Armenian Cup
The Armenian Cup (Armenian: Հայաստանի Անկախության Գավաթ) is the main football cup competition of Armenia. In its original form as the Armenian Cup, it started in 1939, when Armenia was a republic of the Soviet Union. It served as a qualification tournament for the Soviet Cup, and it was not disputed by Armenian teams in the Soviet League pyramid.  After Armenia gained independence in 1992, the cup became known as Independence Cup, and the final is held every year on 9 May.

Since 2022, it has been known as the Fastex Armenian Cup after its headline sponsor.
Camera Obscura (duo)
Camera Obscura are a new wave/synth-pop band formed in 1982 in York, England, by Peter Oldroyd and Nigel James. They signed to Small Wonder Records in 1983 and reached no. 32 on the UK Indie Chart with the single "Destitution". In 1986 the band split, but reformed for a tour of Germany in 2005 after signing to German label Anna Logue Records. They have since released an album of recordings from 1983, Horizons of Suburbia, two singles "Strange Faces" and "Strange Faces 2006" and a live EP from a show in Hannover, Germany.

UK Independent Singles and Albums Charts
The UK Independent Singles Chart and UK Independent Albums Chart are charts of the best-selling independent singles and albums, respectively, in the United Kingdom. Originally published in January 1980, and widely known as the indie chart, the relevance of the chart dwindled in the 1990s as major-label ownership blurred the boundary between independent and major labels.

Separate independent charts are currently published weekly by the Official Charts Company.
Topi Keskinen
Topi Keskinen (born 7 March 2003) is a Finnish professional footballer who plays as a winger for Scottish Premiership club Aberdeen and for the Finland national team. Keskinen is known for his pace, dribbling and agility with the ball.

Finnish League Cup
The Finnish League Cup (in Finnish: Liigacup), is a knock-out football competition contested annually during the pre-season in winter by teams from Veikkausliiga. 
The competition is notably the only football competition in Europe which is mostly played indoors. It is also administrated by Veikkausliiga
Mathilde Hignet
Mathilde Hignet (born 10 June 1993) is a French politician from La France Insoumise. She was elected as the member of parliament for Ille-et-Vilaine's 4th constituency in the 2022 French legislative election.

Ille-et-Vilaine's 4th constituency
The 4th constituency of Ille-et-Vilaine is a French legislative constituency in the Ille-et-Vilaine département. Like the other 576 French constituencies, it elects one MP using the two-round system, with a run-off if no candidate receives over 50% of the vote in the first round.
Keith Schraad
Keith Schraad (born March 14, 1961) is an American politician. He served two years in the Kansas State Senate in 1997 and 1998, where he was the vice-chair of the Judiciary Committee.

After his time in the Senate, Schraad left Kansas and moved to Arizona, where he founded a company called Online Insurance Company from 2008 to 2015. In 2018, he was appointed interim director of the Arizona Department of Insurance by Governor Doug Ducey. He has also worked as the vice president of Blue Cross Blue Shield of Arizona.

Kansas Senate
The Kansas Senate is the upper house of the Kansas Legislature, the state legislature of the U.S. State of Kansas. It is composed of 40 senators elected from single-member districts, each with a population of about 73,000 inhabitants. Members of the Senate are elected to a four-year term. There is no limit to the number of terms that a senator may serve. The Kansas Senate meets at the Kansas State Capitol in Topeka.

Like other upper houses of state and territorial legislatures and the federal U.S. Senate, the Senate is reserved with special functions such as confirming or rejecting gubernatorial appointments to executive departments, the state cabinet, commissions and boards.
Cook Park, Orange
Cook Park is a heritage-listed 4-hectare (10-acre) urban park at 24–26 Summer Street, Orange, a city in the Central West region of New South Wales, Australia. It was designed and built by Alfred Patterson from 1873 to 1950. It is also known as Orange Botanic Garden. It was added to the New South Wales State Heritage Register on 24 August 2018. The park's main entrance is from the corner of Summer Street and Clinton Street.

Quercus robur
Quercus robur, the pedunculate (or "English") oak, is a species of flowering plant in the beech and oak family, Fagaceae. It is a large tree, native to most of Europe, North Africa and western Asia, and is widely cultivated in other temperate regions. It grows on soils of near neutral acidity in the lowlands and is notable for its value to natural ecosystems, supporting a very wide diversity of herbivorous insects and other pests, predators and pathogens.