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Generalization of Measurement-Induced Nonlocality in the Bilocal Scenario

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Abstract

In the paper, we devote to defining an available measure to quantify the nonbilocal correlation in the entanglement-swapping experiment. Then we obtain analytical formulas to calculate the quantifier when the inputs are pure states. For the case of mixed inputs, we discuss the computational properties of the quantifier. Finally, we derive a tight upper bound to the nonbilocality quantifier.

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References

  1. Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Phys. Rev. A 56(2), 1201–1204 (1997)

    Article  ADS  Google Scholar 

  2. Mayers, D., Yao, A.: Quantum cryptography with imperfect apparatus. In: Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) , pp. 503–509. IEEE (1998)

  3. Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98(23), 230501 (2007)

    Article  ADS  Google Scholar 

  4. Pironio, S., Acín, A., Massar, S., Boyer de la Giroday, A., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell’s theorem. Nature 464, 1021–1204 (2010)

    Article  ADS  Google Scholar 

  5. Colbeck, R., Kent, A.: Private randomness expansion with untrusted devices. J. Phys. A: Math. Theor. 44(9), 095305 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  6. Bancal, J.D.: Device-independent witnesses of genuine multipartite entanglement. In: Bancal, J.D. (ed.) On the Device-Independent Approach to Quantum Physics, pp 73–80. Springer, Switzerland (2014)

  7. Brunner, N., Gisin, N., Scarani, V.: Entanglement and non-locality are different resources. New J. Phys. 7, 88–88 (2005)

    Article  ADS  Google Scholar 

  8. Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University, Cambridge (1987)

    MATH  Google Scholar 

  9. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Phys. 1(3), 195–200 (1964)

    Article  MathSciNet  Google Scholar 

  10. Werner, R.F., Wolf, M.M.: Bell inequalities and entanglement. arXiv:quant-ph/0107093 (2001)

  11. Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76(5), 052116 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  12. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  13. Augusiak, R., Cavalcanti, D., Prettico, G., Acín, A.: Perfect quantum privacy implies nonlocality. Phys. Rev. Lett. 104(23), 230401 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  14. Gisin, N., Peres, A.: Maximal violation of Bell’s inequality for arbitrarily large spin. Phys. Lett. A 162(1), 15–17 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  15. Popescu, S., Rohrlich, D.: Generic quantum nonlocality. Phys. Lett. A 166(5-6), 293–297 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  16. Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277–4281 (1989)

    Article  ADS  Google Scholar 

  17. Palazuelos, C.: Superactivation of quantum nonlocality. Phys. Rev. Lett. 109(19), 190401 (2012)

    Article  ADS  Google Scholar 

  18. Peres, A.: All the Bell inequalities. Found. Phys. 29, 589–614 (1999)

    Article  MathSciNet  Google Scholar 

  19. Masanes, L., Liang, Y.C., Doherty, A.C.: All bipartite entangled states display some hidden nonlocality. Phys. Rev. Lett. 100(9), 090403 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  20. Quan, Q., Zhu, H.J., Liu, S.Y., Fei, S.M., Fan, H., Yang, W.L.: Steering Bell-diagonal states. Sci. Rep. 6, 22025 (2016)

    Article  ADS  Google Scholar 

  21. Mor, T.: On classical teleportation and classical non-locality. Int. J. Quantum Inf. 4(1), 161–171 (2006)

    Article  Google Scholar 

  22. Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59(2), 1070–1091 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  23. Horodecki, R., Horodecki, M., Horodecki, P.: Einstein-podolsky-rosen paradox without entanglement. Phys. Rev. A 60(5), 4144–4145 (1999)

    Article  ADS  Google Scholar 

  24. Walgate, J., Hardy, L.: Nonlocality, asymmetry, and distinguishing bipartite states. Phys. Rev. Lett. 89(14), 147901 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  25. Niset, J., Cerf, N.J.: Multipartite nonlocality without entanglement in many dimensions. Phys. Rev. A 74(5), 052103 (2006)

    Article  ADS  Google Scholar 

  26. Luo, S.L., Fu, S.S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106(12), 120401 (2011)

    Article  ADS  Google Scholar 

  27. Dakić, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105(19), 190502 (2010)

    Article  ADS  Google Scholar 

  28. Branciard, C., Gisin, N., Pironio, S.: Characterizing the nonlocal correlations created via entanglement swapping. Phys. Rev. Lett. 104(17), 170401 (2010)

    Article  ADS  Google Scholar 

  29. Branciard, C., Rosset, D., Gisin, N., Pironio, S.: Bilocal versus nonbilocal correlations in entanglement-swapping experiments. Phys. Rev. A 85(3), 032119 (2012)

    Article  ADS  Google Scholar 

  30. Fritz, T.: Beyond Bell’s theorem: correlation scenarios. New J. Phys. 14(10), 103001 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  31. Fritz, T.: Beyond Bell’s theorem II: scenarios with arbitrary causal structure. Commum. Math. Phys. 341, 391–434 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  32. Wood, C.J., Spekkens, R.W.: The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning. New J. Phys. 17(3), 033002 (2015)

    Article  ADS  Google Scholar 

  33. Henson, J., Lal, R., Pusey, M.F.: Theory-independent limits on correlations from generalized Bayesian networks. New J. Phys. 16(11), 113043 (2014)

    Article  ADS  Google Scholar 

  34. Chaves, R., Brask, J.B., Brunner, N.: Device-independent tests of entropy. Phys. Rev. Lett. 115(11), 110501 (2015)

    Article  ADS  Google Scholar 

  35. Tavakoli, A., Skrzypczyk, P., Cavalcanti, D., Acín, A.: Nonlocal correlations in the star-network configuration. Phys. Rev. A 90(6), 062109 (2014)

    Article  ADS  Google Scholar 

  36. Tavakoli, A.: Quantum correlations in connected multipartite Bell experiments. J. Phys. A: Math. Theor. 49(14), 145304 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  37. Tavakoli, A.: Bell-type inequalities for arbitrary noncyclic networks. Phys. Rev. A 93(3), 030101 (2016)

    Article  ADS  Google Scholar 

  38. Chaves, R.: Polynomial Bell inequalities. Phys. Rev. Lett. 116(1), 010402 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  39. Rosset, D., Branciard, C., Barnea, T.J., Pütz, G., Brunner, N., Gisin, N.: Nonlinear Bell inequalities tailored for quantum networks. Phys. Rev. Lett. 116(1), 010403 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  40. Gisin, N., Mei, Q.X., Tavakoli, A., Renou, M.O., Brunner, N.: All entangled pure quantum states violate the bilocality inequality. Phys. Rev. A 96(2), 020304 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

Thanks for comments. The work is supported by National Science Foundation of China under Grant No. 11771011, The Natural Science Foundation of Shanxi Province, China (No.201801D221032) and Scientific and Technological Innovation Programs of Higher Education Instructions in Shanxi (No.2019L0178).

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Authors and Affiliations

  1. College of Information and Computer, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Ying Zhang

  2. College of Mathematics, College of Information and Computer, College of Software, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Kan He

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  1. Ying Zhang
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  2. Kan He
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Correspondence to Kan He.

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Zhang, Y., He, K. Generalization of Measurement-Induced Nonlocality in the Bilocal Scenario. Int J Theor Phys 60, 2178–2192 (2021). https://doi.org/10.1007/s10773-021-04834-9

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