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DOI: 10.4230/LIPIcs.TQC.2017.9

Minimum Quantum Resources for Strong Non-Locality

Authors: Samson Abramsky, Rui Soares Barbosa, Giovanni Carù, Nadish de Silva, Kohei Kishida, and Shane Mansfield

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)

Abstract

We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreasing entanglement between one qubit and the other two, necessitating an increasing number of local measurements on the latter.

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Samson Abramsky, Rui Soares Barbosa, Giovanni Carù, Nadish de Silva, Kohei Kishida, and Shane Mansfield. Minimum Quantum Resources for Strong Non-Locality. In 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abramsky_et_al:LIPIcs.TQC.2017.9,
  author =	{Abramsky, Samson and Barbosa, Rui Soares and Car\`{u}, Giovanni and de Silva, Nadish and Kishida, Kohei and Mansfield, Shane},
  title =	{{Minimum Quantum Resources for Strong Non-Locality}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.9},
  URN =		{urn:nbn:de:0030-drops-85822},
  doi =		{10.4230/LIPIcs.TQC.2017.9},
  annote =	{Keywords: strong non-locality, maximal non-locality, quantum resources, three-qubit states}
}

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DOI: 10.4230/LIPIcs.MFCS.2017.35

The Quantum Monad on Relational Structures

Authors: Samson Abramsky, Rui Soares Barbosa, Nadish de Silva, and Octavio Zapata

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction, and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in information processing tasks. In particular, non-local games have been used to exhibit quantum advantage in boolean constraint satisfaction, and to obtain quantum versions of graph invariants such as the chromatic number. We show how quantum strategies for homomorphism games between relational structures can be viewed as Kleisli morphisms for a quantum monad on the (classical) category of relational structures and homomorphisms. We use these results to exhibit a wide range of examples of contextuality-powered quantum advantage, and to unify several apparently diverse strands of previous work.

Cite as

Samson Abramsky, Rui Soares Barbosa, Nadish de Silva, and Octavio Zapata. The Quantum Monad on Relational Structures. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{abramsky_et_al:LIPIcs.MFCS.2017.35,
  author =	{Abramsky, Samson and Barbosa, Rui Soares and de Silva, Nadish and Zapata, Octavio},
  title =	{{The Quantum Monad on Relational Structures}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.35},
  URN =		{urn:nbn:de:0030-drops-81290},
  doi =		{10.4230/LIPIcs.MFCS.2017.35},
  annote =	{Keywords: non-local games, quantum computation, monads}
}

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Minimum Quantum Resources for Strong Non-Locality

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The Quantum Monad on Relational Structures

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