Advertisement

Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

  • Sutapa Saha
  • Debarshi DasEmail author
  • Souradeep Sasmal
  • Debasis Sarkar
  • Kaushiki Mukherjee
  • Arup Roy
  • Some Sankar Bhattacharya
Article

Abstract

Standard tripartite nonlocality and genuine tripartite nonlocality can be detected by the violations of Mermin inequality and Svetlichny inequality, respectively. Since tripartite quantum nonlocality has novel applications in quantum information and quantum computation, it is important to investigate whether more than three observers can share tripartite nonlocality, simultaneously. In the present study, we answer this question in the affirmative. In particular, we consider a scenario where three spin-\(\frac{1}{2}\) particles are spatially separated and shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle; Bob performs measurements on the second particle, and multiple Charlies perform measurements on the third particle sequentially. In this scenario, we investigate how many Charlies can simultaneously demonstrate standard tripartite nonlocality and genuine tripartite nonlocality with single Alice and single Bob. The interesting result revealed by the present study is that at most six Charlies can simultaneously demonstrate standard tripartite nonlocality with single Alice and single Bob. On the other hand, at most two Charlies can simultaneously demonstrate genuine tripartite nonlocality with single Alice and single Bob. Hence, the present study shows that standard tripartite nonlocality can be simultaneously shared by larger number of Charlies compared to genuine tripartite nonlocality in the aforementioned scenario, which implies that standard tripartite nonlocality is more effective than genuine tripartite nonlocality in the context of simultaneous sharing by multiple observers.

Keywords

Tripartite nonlocality Unsharp measurement Sequential measurement Mermin inequality Svetlichny inequality 

Notes

Acknowledgements

D. D. acknowledges the financial support from University Grants Commission (UGC), Government of India. S. S. acknowledges the financial support from INSPIRE Programme, Department of Science and Technology (DST), Government of India. The authors acknowledge fruitful discussions with Biswajit Paul.

References

  1. 1.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefGoogle Scholar
  2. 2.
    Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1965)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)ADSCrossRefGoogle Scholar
  4. 4.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Acin, A., Ll, M.: Certified randomness in quantum physics. Nature 540, 213 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dusek, M., Lutkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Buhrman, H., Cleve, R., Massar, S., de Wolf, R.: Nonlocality and communication complexity. Rev. Mod. Phys. 82, 665 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    Toner, B., Verstraete, F.: Monogamy of Bell correlations and Tsirelson’s bound. arXiv:quant-ph/0611001 (2006)
  11. 11.
    Silva, R., Gisin, N., Guryanova, Y., Popescu, S.: Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements. Phys. Rev. Lett. 114, 250401 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    Mal, S., Majumdar, A.S., Home, D.: Sharing of nonlocality of a single member of an entangled pair of qubits is not possible by more than two unbiased observers on the other wing. Mathematics 4, 48 (2016)CrossRefGoogle Scholar
  13. 13.
    Hu, M.-J., Zhou, Z.-Y., Hu, X.-M., Li, C.-F., Guo, G.-C., Zhang, Y.-S.: Observation of non-locality sharing among three observers with one entangled pair via optimal weak measurement. NPJ Quantum Inf. 4, 63 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    Schiavon, M., Calderaro, L., Pittaluga, M., Vallone, G., Villoresi, P.: Three-observer Bell inequality violation on a two-qubit entangled state. Quantum Sci. Technol. 2, 015010 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Schrodinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)ADSCrossRefGoogle Scholar
  16. 16.
    Schrodinger, E.: Probability relations between separated systems. Proc. Camb. Philos. Soc. 32, 446 (1936)ADSCrossRefGoogle Scholar
  17. 17.
    Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein–Podolsky–Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A. 76, 052116 (2007)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Sasmal, S., Das, D., Mal, S., Majumdar, A.S.: Steering a single system sequentially by multiple observers. Phys. Rev. A 98, 012305 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    Reid, M.D.: Monogamy inequalities for the Einstein–Podolsky–Rosen paradox and quantum steering. Phys. Rev. A 88, 062108 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    Mal, S., Das, D., Sasmal, S., Majumdar, A.S.: Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering. arXiv:1711.00872 [quant-ph] (2017)
  22. 22.
    Bera, A., Mal, S., De Sen, A., Sen, U.: Witnessing bipartite entanglement sequentially by multiple observers. Phys. Rev. A 98, 062304 (2018)ADSCrossRefGoogle Scholar
  23. 23.
    Mondal, D., Pramanik, T., Pati, A.K.: Nonlocal advantage of quantum coherence. Phys. Rev. A 95, 010301(R) (2017)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Datta, S., Majumdar, A.S.: Sharing of nonlocal advantage of quantum coherence by sequential observers. Phys. Rev. A 98, 042311 (2018)ADSCrossRefGoogle Scholar
  25. 25.
    Mermin, N.D.: Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838 (1990)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Svetlichny, G.: Distinguishing three-body from two-body nonseparability by a Bell-type inequality. Phys. Rev. D 35, 3066 (1987)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Greenberger, D.M., Horne, M.A., Zeilinger, A.: Bells Theorem, Quantum Theory, and Conceptions of the Universe. Springer, Berlin (1989)Google Scholar
  28. 28.
    Ghose, S., Sinclair, N., Debnath, S., Rungta, P., Stock, R.: Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger–Horne–Zeilinger-class states. Phys. Rev. Lett. 102, 250404 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    Ajoy, A., Rungta, P.: Svetlichnys inequality and genuine tripartite nonlocality in three-qubit pure states. Phys. Rev. A 81, 052334 (2010)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Lavoie, J., Kaltenbaek, R., Resch, K.J.: Experimental violation of Svetlichny’s inequality. New J. Phys. 11, 073051 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    Gisin, N.: Bell inequalities: many questions, a few answers. arXiv:quant-ph/0702021 (2007)
  32. 32.
    Seevinck, M., Uffink, J.: Partial separability and entanglement criteria for multiqubit quantum states. Phys. Rev. A 78, 032101 (2008)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Hein, M., Eisert, J., Briegel, H.J.: Multiparty entanglement in graph states. Phys. Rev. A 69, 062311 (2004)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Chen, K., Lo, H.-K.: Multi-partite quantum cryptographic protocols with noisy GHZ States. Quantum Inf. Comput. 7, 689 (2007)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Scarani, V., Gisin, N.: Quantum communication between \(N\) partners and Bell’s inequalities. Phys. Rev. Lett. 87, 117901 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    Seevinck, M. P.: Parts and wholes. An inquiry into quantum and classical correlations. arXiv:0811.1027 [quant-ph] (2009)
  37. 37.
    Zoller, P., et al.: Quantum information processing and communication. Eur. Phys. J. D 36, 203 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    Lu, C.Y., et al.: Experimental entanglement of six photons in graph states. Nature Phys. 3, 91 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    Laflamme, R., et al.: NMR Greenberger–Horne–Zeilinger states. Philos. Trans. R. Soc. A 356, 1941 (1998)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Bouwmeester, D., Pan, J.-W., Daniell, M., Weinfurter, H., Zeilinger, A.: Observation of three-photon Greenberger–Horne–Zeilinger entanglement. Phys. Rev. Lett. 82, 1345 (1999)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Roos, C.F., et al.: Control and measurement of three-qubit entangled states. Science 304, 1478 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    Nelson, R.J., Cory, D.G., Lloyd, S.: Experimental demonstration of Greenberger–Horne–Zeilinger correlations using nuclear magnetic resonance. Phys. Rev. A 61, 022106 (2000)ADSCrossRefGoogle Scholar
  43. 43.
    Sorensen, A.S., Molmer, K.: Entanglement and extreme spin squeezing. Phys. Rev. Lett. 86, 4431 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezze, L., Smerzi, A.: Fisher information and multiparticle entanglement. Phys. Rev. A 85, 022321 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    Toth, G.: Multipartite entanglement and high-precision metrology. Phys. Rev. A 85, 022322 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    Mermin, N.D.: Simple unified form for the major no-hidden-variables theorems. Phys. Rev. Lett. 65, 3373 (1990)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Bancal, J.-D., Barrett, J., Gisin, N., Pironio, S.: Definitions of multipartite nonlocality. Phys. Rev. A 88, 014102 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    Busch, P.: Unsharp reality and joint measurements for spin observables. Phys. Rev. D 33, 2253 (1986)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Busch, P., Grabowski, M., Lathi, P.J.: Operational Quantum Physics. Springer, Berlin (1997)Google Scholar
  50. 50.
    Dur, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    He, Q.Y., Reid, M.D.: Genuine multipartite Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 111, 250403 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    Cavalcanti, D., Skrzypczyk, P.: Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2017)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Jebaratnam, C., Das, D., Roy, A., Mukherjee, A., Bhattacharya, S.S., Bhattacharya, B., Riccardi, A., Sarkar, D.: Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios. Phys. Rev. A 98, 022101 (2018)ADSCrossRefGoogle Scholar
  54. 54.
    Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    Das, D., Datta, S., Goswami, S., Majumdar, A.S., Home, D.: Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation. Phys. Lett. A 381(39), 3396–3404 (2017)ADSCrossRefGoogle Scholar
  56. 56.
    Ardehali, M.: Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Phys. Rev. A 46, 5375 (1992)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    Belinskii, A.V., Klyshko, D.N.: Interference of light and Bell’s theorem. Phys Uspekhi 36, 653 (1993)ADSCrossRefGoogle Scholar
  58. 58.
    Collins, D., Gisin, N., Popescu, S., Roberts, D., Scarani, V.: Bell-type inequalities to detect true \(n\)-body nonseparability. Phys. Rev. Lett. 88, 170405 (2002)ADSCrossRefGoogle Scholar
  59. 59.
    Seevinck, M., Svetlichny, G.: Bell-type inequalities for partial separability in \(N\)-particle systems and quantum mechanical violations. Phys. Rev. Lett. 89, 060401 (2002)ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    Laskowski, W., Zukowski, M.: Detection of \(N\)-particle entanglement with generalized Bell inequalities. Phys. Rev. A 72, 062112 (2005)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia
  2. 2.Centre for Astroparticle Physics and Space Science (CAPSS)Bose InstituteKolkataIndia
  3. 3.Department of Applied MathematicsUniversity of CalcuttaKolkataIndia
  4. 4.Department of MathematicsGovernment Girls’ General Degree CollegeKolkataIndia

Personalised recommendations