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Revealing genuine steering under sequential measurement scenario

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Abstract

Genuine steering is still not well understood enough in contrast to genuine entanglement and nonlocality. Here, we provide a protocol which can reveal genuine steering under some restricted operations compared to the existing witnesses of genuine multipartite steering. Our method has an impression of some sort of ‘hidden’ protocol in the same spirit of hidden nonlocality, which is well understood in bipartite scenario. We also introduce a genuine steering measure which indicates the enhancement of genuine steering in the final state of our protocol compared to the initial states.

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References

  1. Schrödinger, E.: Probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 553 (1935)

    Article  ADS  Google Scholar 

  2. Schrödinger, E.: Probability relations between separated systems. Proc. Camb. Philos. Soc. 32, 446 (1936)

    Article  ADS  Google Scholar 

  3. Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007). https://doi.org/10.1103/PhysRevLett.98.140402

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein–Podolsky–Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76, 052116 (2007). https://doi.org/10.1103/PhysRevA.76.052116

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein–Podolsky–Rosen paradox. Phys. Rev. A 80, 032112 (2009). https://doi.org/10.1103/PhysRevA.80.032112

    Article  ADS  Google Scholar 

  6. Cavalcanti, E.G., He, Q.Y., Reid, M.D., Wiseman, H.M.: Unified criteria for multipartite quantum nonlocality. Phys. Rev. A 84, 032115 (2011). https://doi.org/10.1103/PhysRevA.84.032115

    Article  ADS  Google Scholar 

  7. Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein–Podolsky–Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87, 062103 (2013). https://doi.org/10.1103/PhysRevA.87.062103

    Article  ADS  Google Scholar 

  8. Skrzypczyk, P., Navascues, M., Cavalcanti, D.: Quantifying Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 112, 180404 (2014). https://doi.org/10.1103/PhysRevLett.112.180404

    Article  ADS  Google Scholar 

  9. Gallego, R., Aolita, L.: Resource theory of steering. Phys. Rev. Lett. 5, 041008 (2015). https://doi.org/10.1103/PhysRevX.5.041008

    Article  MATH  Google Scholar 

  10. Kogias, I., Adesso, G.: Einstein–Podolsky–Rosen steering measure for two-mode continuous variable states. J. Opt. Soc. Am. B 32, A27 (2015). https://doi.org/10.1364/JOSAB.32.000A27

    Article  ADS  Google Scholar 

  11. Wittmann, B., Ramelow, S., Steinlechner, F., Langford, N.K., Brunner, N., Wiseman, H., Ursin, R., Zeilinger, A.: Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering. New J. Phys. 14, 053030 (2012). https://doi.org/10.1088/1367-2630/14/5/053030

    Article  ADS  Google Scholar 

  12. Quintino, M.T., Vértesi, T., Brunner, N.: Joint measurability, Einstein–Podolsky–Rosen steering, and Bell nonlocality. Phys. Rev. Lett. 113, 160402 (2014). https://doi.org/10.1103/PhysRevLett.113.160402

    Article  ADS  Google Scholar 

  13. Uola, R., Moroder, T., Gühne, O.: Joint measurability of generalized measurements implies classicality. Phys. Rev. Lett. 113, 160403 (2014). https://doi.org/10.1103/PhysRevLett.113.160403

    Article  ADS  Google Scholar 

  14. Moroder, T., Gittsovich, O., Huber, M., Gühne, O.: Steering bound entangled states: a counterexample to the stronger peres conjecture. Phys. Rev. Lett. 113, 050404 (2014). https://doi.org/10.1103/PhysRevLett.113.050404

    Article  ADS  Google Scholar 

  15. Cavalcanti, E.G., Hall, M.J.W., Wiseman, H.M.: Entanglement verification and steering when Alice and Bob cannot be trusted. Phys. Rev. A 87, 032306 (2013). https://doi.org/10.1103/PhysRevA.87.032306

    Article  ADS  Google Scholar 

  16. Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301 (2012). https://doi.org/10.1103/PhysRevA.85.010301

    Article  ADS  Google Scholar 

  17. Passaro, E., Cavalcanti, D., Skrzypczyk, P., Acín, A.: Optimal randomness certification in the quantum steering and prepare-and-measure scenarios. New J. Phys. 17, 113010 (2015). https://doi.org/10.1088/1367-2630/17/11/113010/meta

    Article  ADS  Google Scholar 

  18. Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 114, 060404 (2015). https://doi.org/10.1103/PhysRevLett.114.060404

    Article  ADS  MathSciNet  Google Scholar 

  19. He, Q., R.-Zárate, L., Adesso, G., Reid, M.D.: Secure continuous variable teleportation and Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 115, 180502 (2015). https://doi.org/10.1103/PhysRevLett.115.180502

    Article  ADS  Google Scholar 

  20. Quintino, M.T., Vértesi, T., Cavalcanti, D., Augusiak, R., Demianowicz, M., Acín, A., Brunner, N.: Inequivalence of entanglement, steering, and Bell nonlocality for general measurements. Phys. Rev. A 92, 032107 (2015). https://doi.org/10.1103/PhysRevA.92.032107

    Article  ADS  Google Scholar 

  21. Popescu, S.: Bell’s inequalities and density matrices: revealing “hidden” nonlocality. Phys. Rev. Lett. 74, 2619 (1995). https://doi.org/10.1103/PhysRevLett.74.2619

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Gisin, N.: Hidden quantum nonlocality revealed by local filters. Phys. Lett. A 210(3), 151–156 (1996). https://doi.org/10.1016/S0375-9601(96)80001-6. 2619

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. He, Q.Y., Reid, M.D.: Genuine multipartite Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 111, 250403 (2013). https://doi.org/10.1103/PhysRevLett.111.250403

    Article  ADS  Google Scholar 

  24. Jebaratnam, C.: Detecting genuine multipartite entanglement in steering scenarios. Phys. Rev. A 93, 052311 (2016). https://doi.org/10.1103/PhysRevA.93.052311

    Article  ADS  Google Scholar 

  25. Augusiak, R., Demianowicz, M., Tura, J., Acín, A.: Entanglement and nonlocality are inequivalent for any number of parties. Phys. Rev. Lett. 115, 030404 (2015). https://doi.org/10.1103/PhysRevLett.115.030404

    Article  ADS  Google Scholar 

  26. Gallego, R., Würflinger, L.E., Acín, A., Navascués, M.: Operational framework for nonlocality. Phys. Rev. Lett. 109, 070401 (2011). https://doi.org/10.1103/PhysRevLett.109.070401

    Article  Google Scholar 

  27. Bancal, J.-D., Barrett, J., Gisin, N., Pironio, S.: Definitions of multipartite nonlocality. Phys. Rev. A 88, 014102 (2013)

    Article  ADS  Google Scholar 

  28. Svetlichny, G.: Distinguishing three-body from two-body nonseparability by a Bell-type inequality. Phys. Rev. D 35, 3066–3069 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  29. Ma, Z.-H., Chen, Z.-H., Chen, J.-L., Spengler, C., Gabriel, A., Huber, M.: Measure of genuine multipartite entanglement with computable lower bounds. Phys. Rev. A 83, 062325 (2011). https://doi.org/10.1103/PhysRevA.83.062325

    Article  ADS  Google Scholar 

  30. Hashemi Rafsanjani, S.M., Huber, M., Broadbent, C.J., Eberly, J.H.: Genuinely multipartite concurrence of \(N\)-qubit \(X\) matrices. Phys. Rev. A 86, 062303 (2012). https://doi.org/10.1103/PhysRevA.86.062303

    Article  ADS  Google Scholar 

  31. Costa, A.C.S., Angelo, R.M.: Quantification of Einstein–Podolsky–Rosen steering for two-qubit states. Phys. Rev. A 93, 020103(R) (2016). https://doi.org/10.1103/PhysRevA.93.020103

    Article  ADS  Google Scholar 

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Acknowledgements

We would like to thank Prof. Guruprasad Kar for useful discussions. We would like to thank Debarshi Das for useful advices. SSB is supported by the John Templeton Foundation through grant 60609, Quantum Causal Structures. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.

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Correspondence to Arup Roy.

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Mukherjee, A., Roy, A., Bhattacharya, S.S. et al. Revealing genuine steering under sequential measurement scenario. Quantum Inf Process 19, 143 (2020). https://doi.org/10.1007/s11128-020-02633-5

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