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Characterizing Bell nonlocality and EPR steering

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Abstract

Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are very important quantum correlations in composite quantum systems. Bell nonlocality of a bipartite state is observed in some local quantum measurements, while EPR steering was first observed by Schrödinger in the context of famous EPR paradox. In this paper, we discuss the Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity as well as the closedness of the sets of all Bell local states and all EPR unsteerable states, respectively. We also derive sufficient conditions for a state to be steerable; these conditions imply that Alice can steer Bob’s state whenever Alice has two POV measurements such that the sets of Bob’s normalized conditional states become two disjoint sets of pure states, or whenever she has one POV measurement such that Bob’s normalized conditional states become a linearly independent set of pure states.

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References

  1. M. S. Blok, N. Kalb, A. Reiserer, T. H. Taminiau, and R. Hanson, Faraday Discuss. 184, 173 (2015).

    Article  ADS  Google Scholar 

  2. D. L. Deng, X. Li, and S. Das Sarma, Phys. Rev. X 7, 021021 (2017), arXiv: 1701.04844.

    Google Scholar 

  3. G. Chiribella, G. M. D’Ariano, and P. Perinotti, Phys. Rev. A 80, 022339 (2009), arXiv: 0904.4483.

    Article  ADS  MathSciNet  Google Scholar 

  4. D. Mulder, and G. Bianconi, arXiv: 1711.06290v3.

  5. C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, Phys. Rev. A 71, 44305 (2005).

    Article  ADS  Google Scholar 

  6. S. M. Zhao, Z. G. Shen, H. Xiao, and L. Wang, Sci. China-Phys. Mech. Astron. 61, 090323 (2018).

    Article  Google Scholar 

  7. S. D. Bartlett, T. Rudolph, and R. W. Spekkens, Rev. Mod. Phys. 79, 555 (2007).

    Article  ADS  Google Scholar 

  8. I. Marvian, and R. W. Spekkens, New J. Phys. 15, 033001 (2013), arXiv: 1104.0018.

    Article  ADS  Google Scholar 

  9. Z. R. Gong, Z. W. Zhang, D. Z. Xu, N. Zhao, and C. P. Sun, Sci. China-Phys. Mech. Astron. 61, 040311 (2018).

    Article  ADS  Google Scholar 

  10. B. Li, S. H. Jiang, S. M. Fei, and X. Q. Li-Jost, Sci. China-Phys. Mech. Astron. 61, 040321 (2018), arXiv: 1801.08476.

    Article  ADS  Google Scholar 

  11. D. P. DiVincenzo, Science 270, 255 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  12. J. Zhou, B. J. Liu, Z. P. Hong, and Z. Y. Xue, Sci. China-Phys. Mech. Astron. 61, 010312 (2018), arXiv: 1705.08852.

    Article  ADS  Google Scholar 

  13. M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information, 2nd ed. (Cambridge University Press, Cambridge, 2010).

    Book  MATH  Google Scholar 

  14. S. Luo, Phys. Rev. A 77, 022301 (2008).

    Article  ADS  Google Scholar 

  15. Z. Guo, H. Cao, and Z. Chen, J. Phys. A-Math. Theor. 45, 145301 (2012).

    Article  ADS  Google Scholar 

  16. Y. C. Wu, and G. C. Guo, Phys. Rev. A 83, 062301 (2011).

    Article  ADS  Google Scholar 

  17. Z. Guo, H. Cao, and S. Qu, Inf. Sci. 289, 262 (2014).

    Article  Google Scholar 

  18. J. S. Bell, Phys. Physique Fizika 1, 195 (1964).

    Article  MathSciNet  Google Scholar 

  19. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014), arXiv: 1303.2849.

    Article  ADS  Google Scholar 

  20. J. F. Clauser, and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).

    Article  ADS  Google Scholar 

  21. D. Home, and F. Selleri, Riv. Nuovo Cim. 14, 1 (1991).

    Article  Google Scholar 

  22. L. A. Khalfin, and B. S. Tsirelson, Found Phys. 22, 879 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  23. B. S. Tsirelson, Hadronic J. Suppl. 8, 329 (1993).

    MathSciNet  Google Scholar 

  24. A. Zeilinger, Rev. Mod. Phys. 71, S288 (1999).

    Article  Google Scholar 

  25. R. F. Werner, and M. M. Wolf, Phys. Rev. A 64, 032112 (2001).

    Article  ADS  Google Scholar 

  26. M. Genovese, Phys. Rep. 413, 319 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  27. H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, Rev. Mod. Phys. 82, 665 (2010), arXiv: 0907.3584; Z. Chen and Y. J. Han, Chin. Sci. Bull. 61, 1072 (2016).

    Article  ADS  Google Scholar 

  28. L. J. Zhao, Y. M. Guo, X. Q. Li-Jost, and S. M. Fei, Sci. China-Phys. Mech. Astron. 61, 070321 (2018).

    Article  ADS  Google Scholar 

  29. Y. Yang, H. Cao, L. Chen, and Y. Huang, Int. J. Theor. Phys. 57, 1498 (2018).

    Article  Google Scholar 

  30. G. L. Long, W. Qin, Z. Yang, and J. L. Li, Sci. China-Phys. Mech. Astron. 61, 030311 (2018).

    Article  ADS  Google Scholar 

  31. E. Schrödinger, and M. Born, Math. Proc. Camb. Phil. Soc. 31, 555 (1935).

    Article  ADS  Google Scholar 

  32. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

    Article  ADS  Google Scholar 

  33. M. D. Reid, Phys. Rev. A 40, 913 (1989).

    Article  ADS  Google Scholar 

  34. R. F. Werner, Phys. Rev. A 40, 4277 (1989).

    Article  ADS  Google Scholar 

  35. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).

    Article  ADS  Google Scholar 

  36. H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  37. E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid, Phys. Rev. A 80, 032112 (2009), arXiv: 0907.1109.

    Article  ADS  Google Scholar 

  38. D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, Nat. Phys. 6, 845 (2010), arXiv: 0909.0805.

    Article  Google Scholar 

  39. A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, Phys. Rev. X 2, 031003 (2012), arXiv: 1111.0739.

    Google Scholar 

  40. V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, Nat. Photon 6, 596 (2012).

    Article  Google Scholar 

  41. C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, Phys. Rev. A 85, 010301(R) (2012), arXiv: 1109.1435.

    Article  ADS  Google Scholar 

  42. B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, New J. Phys. 14, 053030 (2012), arXiv: 1111.0760.

    Article  ADS  Google Scholar 

  43. S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, Phys. Rev. A 87, 022104 (2013), arXiv: 1112.0461.

    Article  ADS  Google Scholar 

  44. M. D. Reid, Phys. Rev. A 88, 062338 (2013), arXiv: 1402.4235.

    Article  ADS  Google Scholar 

  45. P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Phys. Rev. Lett. 112, 180404 (2014), arXiv: 1311.4590.

    Article  ADS  Google Scholar 

  46. M. Piani, and J. Watrous, Phys. Rev. Lett. 114, 060404 (2015), arXiv: 1406.0530.

    Article  ADS  MathSciNet  Google Scholar 

  47. M. Żukowski, A. Dutta, and Z. Yin, Phys. Rev. A 91, 032107 (2015), arXiv: 1411.5986.

    Article  ADS  MathSciNet  Google Scholar 

  48. M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, Phys. Rev. A 92, 032107 (2015), arXiv: 1501.03332.

    Article  ADS  Google Scholar 

  49. H. Zhu, M. Hayashi, and L. Chen, Phys. Rev. Lett. 116, 070403 (2016).

    Article  ADS  Google Scholar 

  50. K. Sun, X. J. Ye, J. S. Xu, X. Y. Xu, J. S. Tang, Y. C. Wu, J. L. Chen, C. F. Li, and G. C. Guo, Phys. Rev. Lett. 116, 160404 (2016), arXiv: 1511.01679.

    Article  ADS  Google Scholar 

  51. Q. Quan, H. Zhu, S. Y. Liu, S. M. Fei, H. Fan, and W. L. Yang, Sci. Rep. 6, 22025 (2016), arXiv: 1601.00113.

    Article  ADS  Google Scholar 

  52. J. L. Chen, C. Ren, C. Chen, X. J. Ye, and A. K. Pati, Sci. Rep. 6, 39063 (2016), arXiv: 1606.07060.

    Article  ADS  Google Scholar 

  53. D. Cavalcanti, and P. Skrzypczyk, Rep. Prog. Phys. 80, 024001 (2017), arXiv: 1604.00501.

    Article  ADS  Google Scholar 

  54. D. Das, S. Datta, C. Jebaratnam, A. S. Majumdar, Phys. Rev. A 97, 022110 (2018).

    Article  ADS  Google Scholar 

  55. C. Ren, H. Y. Su, H. Shi, and J. Chen, Phys. Rev. A 97, 032119 (2018).

    Article  ADS  Google Scholar 

  56. C. Zheng, Z. Guo, and H. Cao, Int. J. Theor. Phys. 57, 1787 (2018).

    Article  Google Scholar 

  57. M. J. Zhao, T. Ma, T. G. Zhang, and S. M. Fei, Sci. China-Phys. Mech. Astron. 59, 120313 (2016), arXiv: 1610.08146.

    Article  ADS  Google Scholar 

  58. H. X. Cao, Sci. China-Phys. Mech. Astron. 60, 020332 (2017).

    Article  ADS  Google Scholar 

  59. S. J. Wei, T. Xin, and G. L. Long, Sci. China-Phys. Mech. Astron. 61, 070311 (2018), arXiv: 1706.08080.

    Article  ADS  Google Scholar 

  60. S. Yu, Q. Chen, C. Zhang, C. H. Lai, and C. H. Oh, Phys. Rev. Lett. 109, 120402 (2012), arXiv: 1205.1179.

    Article  ADS  Google Scholar 

  61. C. Wu, J. L. Chen, X. J. Ye, H. Y. Su, D. L. Deng, Z. Wang, and C. H. Oh, Sci. Rep. 4, 4291 (2015), arXiv: 1402.3442.

    Article  Google Scholar 

  62. Z. Guo, H. Cao, and S. Qu, Found Phys. 45, 355 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  63. J. L. Chen, X. J. Ye, C. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, Sci. Rep. 3, 2143 (2013), arXiv: 1204.1870.

    Article  Google Scholar 

  64. H. C. Nguyen, and K. Luoma, Phys. Rev. A 95, 042117 (2017).

    Article  ADS  Google Scholar 

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  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    HuaiXin Cao & ZhiHua Guo

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  1. HuaiXin Cao
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Cao, H., Guo, Z. Characterizing Bell nonlocality and EPR steering. Sci. China Phys. Mech. Astron. 62, 30311 (2019). https://doi.org/10.1007/s11433-018-9279-4

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