Minimum Quantum Resources for Strong Non-Locality

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



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Samson Abramsky
Rui Soares Barbosa
Giovanni Carù
Nadish de Silva
Kohei Kishida
Shane Mansfield

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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)
https://doi.org/10.4230/LIPIcs.TQC.2017.9

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.
Keywords
  • strong non-locality
  • maximal non-locality
  • quantum resources
  • three-qubit states

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References

  1. Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield. Contextuality, cohomology and paradox. In Stephan Kreutzer, editor, 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, September 7-10, 2015, Berlin, Germany, volume 41 of LIPIcs, pages 211-228. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2015. URL: http://dx.doi.org/10.4230/LIPIcs.CSL.2015.211.
  2. Samson Abramsky, Rui Soares Barbosa, and Shane Mansfield. The contextual fraction as a measure of contextuality. to appear, 2017. Google Scholar
  3. Samson Abramsky and Adam Brandenburger. The sheaf-theoretic structure of non-locality and contextuality. New Journal of Physics, 13(11):113036, 2011. URL: http://dx.doi.org/10.1088/1367-2630/13/11/113036.
  4. Samson Abramsky, Carmen M. Constantin, and Shenggang Ying. Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states. Information and Computation, 250:3-14, 2016. Google Scholar
  5. Samson Abramsky, Shane Mansfield, and Rui Soares Barbosa. The cohomology of non-locality and contextuality. In Bart Jacobs, Peter Selinger, and Bas Spitters, editors, Proceedings 8th International Workshop on Quantum Physics and Logic, QPL 2011, Nijmegen, Netherlands, October 27-29, 2011., volume 95 of EPTCS, pages 1-14, 2011. URL: http://dx.doi.org/10.4204/EPTCS.95.1.
  6. Janet Anders and Dan E. Browne. Computational power of correlations. Physical Review Letters, 102:050502, Feb 2009. URL: http://dx.doi.org/10.1103/PhysRevLett.102.050502.
  7. Leandro Aolita, Rodrigo Gallego, Antonio Acín, Andrea Chiuri, Giuseppe Vallone, Paolo Mataloni, and Adán Cabello. Fully nonlocal quantum correlations. Physical Review A, 85(3):032107, Mar 2012. URL: http://dx.doi.org/10.1103/PhysRevA.85.032107.
  8. Jonathan Barrett, Adrian Kent, and Stefano Pironio. Maximally nonlocal and monogamous quantum correlations. Physical Review Letters, 97(17):170409, Oct 2006. URL: http://dx.doi.org/10.1103/PhysRevLett.97.170409.
  9. John S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1(3):195-200, 1964. Google Scholar
  10. Charles H. Bennett, Herbert J. Bernstein, Sandu Popescu, and Benjamin Schumacher. Concentrating partial entanglement by local operations. Physical Review A, 53:2046-2052, Apr 1996. URL: http://dx.doi.org/10.1103/PhysRevA.53.2046.
  11. Charles H. Bennett, Sandu Popescu, Daniel Rohrlich, John A. Smolin, and Ashish V. Thapliyal. Exact and asymptotic measures of multipartite pure-state entanglement. Physical Review A, 63:012307, Dec 2000. URL: http://dx.doi.org/10.1103/PhysRevA.63.012307.
  12. Gilles Brassard, André Allan Méthot, and Alain Tapp. Minimum entangled state dimension required for pseudo-telepathy. Quantum Information & Computation, 5(4):275-284, Jul 2005. Google Scholar
  13. John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23(15):880-884, Oct 1969. URL: http://dx.doi.org/10.1103/PhysRevLett.23.880.
  14. Vedran Dunjko, Theodoros Kapourniotis, and Elham Kashefi. Quantum-enhanced secure delegated classical computing. Quantum Information & Computation, 61(1):61-86, Jan 2016. Google Scholar
  15. W. Dür, G. Vidal, and J. I. Cirac. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A, 62:062314, Nov 2000. URL: http://dx.doi.org/10.1103/PhysRevA.62.062314.
  16. Avshalom C. Elitzur, Sandu Popescu, and Daniel Rohrlich. Quantum nonlocality for each pair in an ensemble. Phys. Lett. A, 162(1):25-28, 1992. URL: http://dx.doi.org/10.1016/0375-9601(92)90952-I.
  17. Arthur Fine. Hidden variables, joint probability, and the Bell inequalities. Physical Review Letters, 48(5):291-295, Feb 1982. URL: http://dx.doi.org/10.1103/PhysRevLett.48.291.
  18. Daniel M. Greenberger, Michael A. Horne, Abner Shimony, and Anton Zeilinger. Bell’s theorem without inequalities. American Journal of Physics, 58(12):1131-1143, 1990. URL: http://dx.doi.org/10.1119/1.16243.
  19. Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger. Going beyond Bell’s theorem. In M. Kafatos, editor, Bell’s theorem, quantum theory, and conceptions of the universe, pages 69-72. Kluwer, 1989. Google Scholar
  20. Otfried Gühne, Géza Tóth, Philipp Hyllus, and Hans J. Briegel. Bell inequalities for graph states. Physical Review Letters, 95:120405, Sep 2005. URL: http://dx.doi.org/10.1103/PhysRevLett.95.120405.
  21. Lucien Hardy. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Physical Review Letters, 68(20):2981-2984, May 1992. URL: http://dx.doi.org/10.1103/PhysRevLett.68.2981.
  22. Lucien Hardy. Nonlocality for two particles without inequalities for almost all entangled states. Physical Review Letters, 71(11):1665-1668, 1993. Google Scholar
  23. Peter Heywood and Michael L. G. Redhead. Nonlocality and the Kochen-Specker paradox. Foundations of physics, 13(5):481-499, 1983. URL: http://dx.doi.org/10.1007/BF00729511.
  24. Adrian Kent, Noah Linden, and Serge Massar. Optimal entanglement enhancement for mixed states. Physical Review Letters, 83:2656-2659, Sep 1999. URL: http://dx.doi.org/10.1103/PhysRevLett.83.2656.
  25. Laura Mančinska, David E. Roberson, and Antonios Varvitsiotis. On deciding the existence of perfect entangled strategies for nonlocal games. Chicago Journal of Theoretical Computer Science, 2016(5):1-16, Apr 2016. Google Scholar
  26. Shane Mansfield. Consequences and applications of the completeness of Hardy’s nonlocality. Physical Review A, 95:022122, Feb 2017. URL: http://dx.doi.org/10.1103/PhysRevA.95.022122.
  27. N. David Mermin. Quantum mysteries revisited. American Journal of Physics, 58(8):731-734, 1990. URL: http://dx.doi.org/10.1119/1.16503.
  28. N. David Mermin. Simple unified form for the major no-hidden-variables theorems. Physical Review Letters, 65(27):3373-3376, Dec 1990. URL: http://dx.doi.org/10.1103/PhysRevLett.65.3373.
  29. M. A. Nielsen. Conditions for a class of entanglement transformations. Physical Review Letters, 83:436-439, Jul 1999. URL: http://dx.doi.org/10.1103/PhysRevLett.83.436.
  30. Robert Raussendorf. Contextuality in measurement-based quantum computation. Physical Review A, 88:022322, Aug 2013. URL: http://dx.doi.org/10.1103/PhysRevA.88.022322.
  31. Robert Raussendorf and Hans J. Briegel. A one-way quantum computer. Physical Review Letters, 86:5188-5191, May 2001. URL: http://dx.doi.org/10.1103/PhysRevLett.86.5188.
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