No Access

Revisited aspects of the local set in CHSH Bell scenario

Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

International Centre for Theory of Quantum Technologies, University of Gdansk, Jana Bażyńskiego 1A, 80-309 Gdansk, Poland

Search for more papers by this author

, and

Antonio Mandarino

International Centre for Theory of Quantum Technologies, University of Gdansk, Jana Bażyńskiego 1A, 80-309 Gdansk, Poland

E-mail Address: [email protected]

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219749923400051Cited by:3 (Source: Crossref)

This article is part of the issue:

Special Issue: Quantum Lectures
Guest Editors: Alessio Avella, Fabrizio Piacentini, Marco Gramegna, Ivano Ruo Berchera, Milena D'Angelo, Francesco V. Pepe and Paolo Olivero

Abstract

The Bell inequalities stand at the cornerstone of the developments of quantum theory on both the foundational and applied side. The discussion started as a way to test whether the quantum description of reality is complete or not, but it developed in such a way that a new research area stemmed from it, namely quantum information. Far from being and exhausted topic, in this paper, we present a constructive and geometrically intuitive description of the local polytope and its facets in a bipartite Bell scenario with two dichotomic measurements per party.

Keywords:

References

1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, 1964). Google Scholar
2. J. S. Bell, Phys. Phys. Fiz. 1 (1964) 195. Crossref, Google Scholar
3. J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23 (1969) 880. Crossref, Web of Science, Google Scholar
4. J. F. Clauser and M. A. Horne, Phys. Rev. D 10 (1974) 526. Crossref, Web of Science, Google Scholar
5. M. Bavarian and P. W. Shor, Information Causality, Szemerédi-Trotter and algebraic variants of CHSH, in Proc. 2015 Conf. Innovations in Theoretical Computer Science, ITCS ’15 (ACM, New York, NY, USA, 2015), pp. 123–132. Google Scholar
6. A. Peres and D. R. Terno, Rev. Mod. Phys. 76 (2004) 93. Crossref, Web of Science, Google Scholar
7. J. Barrett, L. Hardy and A. Kent, Phys. Rev. Lett. 95 (2005) 010503. Crossref, Web of Science, Google Scholar
8. T. Cope and R. Colbeck, Phys. Rev. A 100 (2019) 022114. Crossref, Web of Science, Google Scholar
9. S. Pironio, J. Phys. A: Math. Theor. 47 (2014) 424020. Crossref, Web of Science, Google Scholar
10. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani and S. Wehner, Rev. Mod. Phys. 86 (2014) 419. Crossref, Web of Science, Google Scholar
11. G. M. Ziegler, Lectures on Polytopes (Springer, New York, 1995). Crossref, Google Scholar
12. J. A. Green, Math. Z. 70 (1958) 430. Crossref, Google Scholar
13. D. Avis and K. Fukuda, Discrete Comput. Geom. 8 (1992) 295. Crossref, Web of Science, Google Scholar
14. E. W. Weisstein, CRC Concise Encyclopedia of Mathematics CD-ROM (CRC, 2002). Crossref, Google Scholar
15. L. Khachiyan, E. Boros, K. Borys, K. Elbassioni and V. Gurvich, Discrete Comput. Geom. 39 (2008) 174. Crossref, Web of Science, Google Scholar
16. A. Fine, Phys. Rev. Lett. 48 (1982) 291. Crossref, Web of Science, Google Scholar
17. S. Pironio, J. Math. Phys. 46 (2005) 062112. Crossref, Web of Science, Google Scholar
18. J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu and D. Roberts, Phys. Rev. A 71 (2005) 022101. Crossref, Web of Science, Google Scholar
19. S. Popescu and D. Rohrlich, Found. Phys. 24 (1994) 379. Crossref, Web of Science, Google Scholar
20. V. Scarani, Bell Nonlocality (Oxford University Press, 2019). Crossref, Google Scholar
21. C. J. Wood and R. W. Spekkens, New J. Phys. 17 (2015) 033002. Crossref, Web of Science, Google Scholar
22. G. Chiribella, G. M. D’ Ariano and P. Perinotti, Phys. Rev. A 81 (2010) 062348. Crossref, Web of Science, Google Scholar
23. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio and V. Scarani, Phys. Rev. Lett. 98 (2007) 230501. Crossref, Web of Science, Google Scholar
24. L. Masanes, S. Pironio and A. Acín, Nat. Commun. 2 (2011) 1. Crossref, Web of Science, Google Scholar
25. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis. Volume 1: Metric and Normed Spaces (Graylock Press, Rochester, 1957). Google Scholar
26. R. Chaves, Phys. Rev. Lett. 116 (2016) 010402. Crossref, Web of Science, Google Scholar
27. J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu and D. Roberts, Phys. Rev. A 71 (2005) 022101. Crossref, Web of Science, Google Scholar
28. R. F. Werner and M. M. Wolf, Phys. Rev. A 64 (2001) 032112. Crossref, Web of Science, Google Scholar
29. M. Żukowski and C. Brukner, Phys. Rev. Lett. 88 (2002) 210401. Crossref, Web of Science, Google Scholar
30. A. Mandarino and G. Scala, Entropy 25 (2023) 94. Crossref, Web of Science, Google Scholar
31. M. Karczewski, G. Scala, A. Mandarino, A. B. Sainz and M. Zukowski, J. Phys. A: Math. Theor. 55 (2022) 384011. Crossref, Web of Science, Google Scholar
32. D. Chruściński and G. Sarbicki, J. Phys. A: Math. Theor. 47 (2014) 483001. Crossref, Web of Science, Google Scholar
33. G. Sarbicki, G. Scala and D. Chruściński, Phys. Rev. A 101 (2020) 012341. Crossref, Web of Science, Google Scholar
34. G. Sarbicki, G. Scala and D. Chruściński, J. Phys. A: Math. Theor. 53 (2020) 455302. Crossref, Web of Science, Google Scholar
35. T. Das, M. Karczewski, A. Mandarino, M. Markiewicz, B. Woloncewicz and M. Żukowski, New J. Phys. 24 (2022) 033017. Crossref, Web of Science, Google Scholar
36. T. Das, M. Karczewski, A. Mandarino, M. Markiewicz, B. Woloncewicz and M. Żukowski, New J. Phys. 23 (2021) 073042. Crossref, Web of Science, Google Scholar
37. T. Das, M. Karczewski, A. Mandarino, M. Markiewicz, B. Woloncewicz and M. Zukowski, Phys. Lett. A 435 (2022) 128031. Crossref, Web of Science, Google Scholar
38. T. Das, M. Karczewski, A. Mandarino, M. Markiewicz, B. Woloncewicz and M. Żukowski, New J. Phys. 24 (2022) 038001. Crossref, Web of Science, Google Scholar
39. T. Das, M. Karczewski, A. Mandarino, M. Markiewicz and M. Żukowski, Phys. Rev. Appl. 18 (2022) 034074. Crossref, Web of Science, Google Scholar
40. K. Schlichtholz, A. Mandarino and M. Żukowski, New J. Phys. 24 (2022) 103003. Crossref, Web of Science, Google Scholar
41. L. Catani, M. Leifer, G. Scala, D. Schmid and R. W. Spekkens, Phys. Rev. Lett. 129 (2022) 240401. Crossref, Web of Science, Google Scholar
42. R. W. Spekkens, D. H. Buzacott, A. J. Keehn, B. Toner and G. J. Pryde, Phys. Rev. Lett. 102 (2009) 010401. Crossref, Web of Science, Google Scholar