Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Measurement incompatibility at all remote parties do not always permit Bell nonlocality (2312.15705v2)

Published 25 Dec 2023 in quant-ph

Abstract: Two important ingredients necessary for obtaining Bell nonlocal correlations between two spatially separated parties are an entangled state shared between them and an incompatible set of measurements employed by each of them. We focus on the relation of Bell nonlocality with incompatibility of the set of measurements employed by both the parties, in the two-input and two-output scenario. We first observe that Bell nonlocality can always be established when both parties employ any set of incompatible projective measurements. On the other hand, going beyond projective measurements, we present a class of incompatible positive operator-valued measures, employed by both the observers, which can never activate Bell nonlocality. Furthermore, we find a sufficient criterion for achieving Bell nonlocal correlations given a fixed amount of pure two-qubit entanglement and a fixed amount of incompatibility of projective measurements applied by either both parties or a single party.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (51)
  1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, 2nd ed. (Cambridge University Press, 2004).
  2. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani,  and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419 (2014).
  3. S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938 (1972).
  4. A. Aspect, P. Grangier,  and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460 (1981).
  5. A. Aspect, P. Grangier,  and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91 (1982a).
  6. A. Aspect, J. Dalibard,  and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804 (1982b).
  7. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter,  and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
  8. M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe,  and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791 (2001).
  9. The BIG Bell Test Collaboration, “Challenging local realism with human choices,” Nature 557, 212 (2018).
  10. S. Storz, J. Schär, A. Kulikov, P. Magnard, P. Kurpiers, J. Lütolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, J. Besse, M. Gabureac, G. J. Norris, A. Rosario, F. Martin, J. Martinez, W. Amaya, M. W. Mitchell, C. Abellan, J. Bancal, N. Sangouard, B. Royer, A. Blais,  and A. Wallraff, “Loophole-free Bell inequality violation with superconducting circuits,” Nature 617, 265 (2023).
  11. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio,  and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).
  12. S. Pironio, A. Acín, N. Brunner, N. Gisin, S. Massar,  and V. Scarani, “Device-independent quantum key distribution secure against collective attacks,” New J. Phys. 11, 045021 (2009).
  13. E. Woodhead, A. Acín,  and S. Pironio, “Device-independent quantum key distribution with asymmetric CHSH inequalities,” Quantum 5, 443 (2021).
  14. M. Farkas, M. Balanzó-Juandó, K. Łukanowski, J. Kołodyński,  and A. Acín, “Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols,” Phys. Rev. Lett. 127, 050503 (2021).
  15. L. Wooltorton, P. Brown,  and R. Colbeck, “Device-independent quantum key distribution with arbitrarily small nonlocality,”  (2023), arXiv:2309.09650 [quant-ph] .
  16. M. Farkas, “Unbounded device-independent quantum key rates from arbitrarily small non-locality,”  (2023), arXiv:2310.08635 [quant-ph] .
  17. S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning,  and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021 (2010).
  18. R. Colbeck and A. Kent, “Private randomness expansion with untrusted devices,” J. Phys. A Math. Theor. 44, 095305 (2011).
  19. Y. Liu, Q. Zhao, M. Li, J. Guan, B. Zhang, Y.and Bai, W. Zhang, W. Liu, C. Wu, X. Yuan, H. Li, W. J. Munro, Z. Wang, L. You, J. Zhang, X. Ma, J. Fan, Q. Zhang,  and J-W. Pan, “Device-independent quantum random-number generation,” Nature 562, 548 (2018).
  20. L. Wooltorton, P. Brown,  and R. Colbeck, “Tight analytic bound on the trade-off between device-independent randomness and nonlocality,” Phys. Rev. Lett. 129, 150403 (2022).
  21. R. Horodecki, P. Horodecki, M. Horodecki,  and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
  22. O. Gühne and G. Tóth, “Entanglement detection,” Phys. Rep. 474, 1 (2009).
  23. P. Busch, “Unsharp reality and joint measurements for spin observables,” Phys. Rev. D 33, 2253 (1986).
  24. P. Lahti, “Coexistence and joint measurability in quantum mechanics,” Int. J. Theor. Phys. 42, 893 (2003).
  25. T. Heinosaari, D. Reitzner,  and P. Stano, “Notes on joint measurability of quantum observables,” Found. Phys. 38, 1133 (2008).
  26. S. T. Ali, C. Carmeli, T. Heinosaari,  and A. Toigo, “Commutative POVMs and fuzzy observables,” Found. Phys. 39, 593 (2009).
  27. T. Heinosaari and M. M. Wolf, “Nondisturbing quantum measurements,” J. Math. Phys. 51, 092201 (2010).
  28. T. Heinosaari, T. Miyadera,  and M. Ziman, “An invitation to quantum incompatibility,” J. Phys. A Math. Theor. 49, 123001 (2016).
  29. O. Gühne, E. Haapasalo, T. Kraft, J. Pellonpää,  and R. Uola, “Colloquium: Incompatible measurements in quantum information science,” Rev. Mod. Phys. 95, 011003 (2023).
  30. R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277 (1989).
  31. J. Barrett, “Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality,” Phys. Rev. A 65, 042302 (2002).
  32. S. Popescu, “Bell’s inequalities versus teleportation: What is nonlocality?” Phys. Rev. Lett. 72, 797 (1994).
  33. S. Popescu, “Bell’s inequalities and density matrices: Revealing “hidden” nonlocality,” Phys. Rev. Lett. 74, 2619 (1995).
  34. R. Horodecki, P. Horodecki,  and M. Horodecki, “Violating Bell inequality by mixed spin-1/2 states: necessary and sufficient condition,” Phys. Lett. A 200, 340 (1995).
  35. N. Gisin, “Hidden quantum nonlocality revealed by local filters,” Phys. Lett. A 210, 151 (1996).
  36. A. Peres, “Collective tests for quantum nonlocality,” Phys. Rev. A 54, 2685 (1996).
  37. E. Bene and T. Vértesi, “Measurement incompatibility does not give rise to Bell violation in general,” New J. Phys. 20, 013021 (2018).
  38. F. Hirsch, M. T. Quintino,  and N. Brunner, “Quantum measurement incompatibility does not imply Bell nonlocality,” Phys. Rev. A 97, 012129 (2018).
  39. M. M. Wolf, D. Perez-Garcia,  and C. Fernandez, “Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory,” Phys. Rev. Lett. 103, 230402 (2009).
  40. J. F. Clauser, M. A. Horne, A. Shimony,  and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
  41. D. Collins, N. Gisin, N. Linden, S. Massar,  and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
  42. J. Chen, C. Wu, L. C. Kwek, D. Kaszlikowski, M. Żukowski,  and C. H. Oh, “Multicomponent Bell inequality and its violation for continuous-variable systems,” Phys. Rev. A 71, 032107 (2005).
  43. E. G. Cavalcanti, C. J. Foster, M. D. Reid,  and P. D. Drummond, “Bell inequalities for continuous-variable correlations,” Phys. Rev. Lett. 99, 210405 (2007).
  44. A. Salles, D. Cavalcanti, A. Acín, D. Pérez-García,  and M. M. Wolf, “Bell inequalities from multilinear contractions,” Quantum Inf. Comput. 10, 703 (2010).
  45. L. J. Landau, “On the violation of Bell’s inequality in quantum theory,” Phys. Lett. A 120, 54 (1987).
  46. M. A. Nielsen, “Conditions for a class of entanglement transformations,” Phys. Rev. Lett. 83, 436 (1999).
  47. G. Vidal, “Entanglement of pure states for a single copy,” Phys. Rev. Lett. 83, 1046 (1999).
  48. D. Jonathan and M. B. Plenio, “Minimal conditions for local pure-state entanglement manipulation,” Phys. Rev. Lett. 83, 1455 (1999).
  49. L. Hardy, “Method of areas for manipulating the entanglement properties of one copy of a two-particle pure entangled state,” Phys. Rev. A 60, 1912 (1999).
  50. G. Vidal, “Entanglement monotones,” J. Mod. Opt. 47, 355 (2000).
  51. H. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now