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Hierarchy in loss of nonlocal correlations of two-qubit states in noisy environments

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Abstract

Composite quantum systems exhibit nonlocal correlations. These counterintuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two-qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportation, states that violate Bell-CHSH inequality, and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two-qubit states that exhibit higher-order nonlocal correlations. We find that loss of nonlocal correlations in the presence of noise follows the same hierarchy, that is, higher-order nonlocal correlation disappears for small strength of noise, whereas lower-order nonlocal correlations survive strong noisy environment. We show this results for decoherence due to amplitude damping channel on various quantum states. However, we observe that same hierarchy is followed by states undergoing decoherence due to phase damping as well as depolarizing channels.

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References

  1. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wooters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1965)

    Google Scholar 

  4. 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)

    Article  ADS  Google Scholar 

  5. Reinhard, F.: Werner, quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

  6. Hardy, L.: Disentangling nonlocality and teleportation. arxiv:quant-ph/9906123 (1999)

  7. Zukowski, M.: Bell theorem for the nonclassical part of the quantum teleportation process. Phys. Rev. A 60, 032101 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  8. Popescu, S.: Bells inequalities versus teleportation: What is nonlocality? Phys. Rev. Lett. 72, 797 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Horodecki, R., Horodecki, M., Horodecki, P.: Teleportation, Bell’s inequalities and inseparability. Phys. Lett. A 21, 222 (1996)

    MathSciNet  MATH  Google Scholar 

  10. Hu, M.-L.: Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states. Quantum Inf. Process. 12, 229 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Gisin, N.: Nonlocality criteria for quantum teleportation. Phys. Lett. A 210, 157 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Barret, J.: Implications of teleportation for nonlocality. Phys. Rev. A 64, 042305 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  13. Paulson, K.G., Satyanarayana, S.V.M.: Relevance of rank for mixed state quantum teleportation resource. Quantum Inf. Comput. 14, 1227 (2014)

    MathSciNet  Google Scholar 

  14. Wootters, W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27 (2001)

    MathSciNet  MATH  Google Scholar 

  15. Bandyopadhyay, S., Ghosh, A.: Optimal fidelity for a quantum channel may be attained by nonmaximally entangled states. Phys. Rev. A 86, 020304(R) (2012)

    Article  ADS  Google Scholar 

  16. Wang, Q., Tan, M.-Y., Liu, Y., Zeng, H.-S.: Entanglement distribution via noisy quantum channels. J. Phys. B At. Mol. Opt. Phys. 42, 125503 (2009)

    Article  ADS  Google Scholar 

  17. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  18. Srikanth, R., Banarjee, S.: Squeezed generalized amplitude damping channel. Phys. Rev. A. 77, 012318 (2008)

    Article  ADS  Google Scholar 

  19. Li, Y.-L., Xiao, X.: Recovering quantum correlations from amplitude damping decoherence by weak measurement reversal. Quantum Inf. Process. 12, 3067 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Isizaka, S., Hiroshima, T.: Maximally entangled mixed states under nonlocal unitary operations in two qubits. Phys. Rev. A 62, 022310 (2000)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Pondicherry University, Puducherry, 605014, India

    K. G. Paulson & S. V. M. Satyanarayana

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  1. K. G. Paulson
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  2. S. V. M. Satyanarayana
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Correspondence to S. V. M. Satyanarayana.

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Paulson, K.G., Satyanarayana, S.V.M. Hierarchy in loss of nonlocal correlations of two-qubit states in noisy environments. Quantum Inf Process 15, 1639–1647 (2016). https://doi.org/10.1007/s11128-015-1236-1

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  • DOI: https://doi.org/10.1007/s11128-015-1236-1

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