Revealing quantum correlation by negativity of the Wigner function

Revealing quantum correlation by negativity of the Wigner function We analyze two two-mode continuous variable separable states with the same marginal states. We adopt the definition of classicality in the form of well-defined positive Wigner function describing the state and find that although the states possess positive local Wigner functions, they exhibit negative Wigner functions for the global states. Using the negativity of Wigner function as an indicator of nonclassicality, we show that despite these states possess different negativities of the Wigner function, they do not reveal this difference as phase space nonclassicalities such as negativity of the Mandel Q parameter or quadrature squeezing. We then concentrate on quantum correlation of these states and show that quantum discord and local quantum uncertainty, as two well-defined measures of quantum correlation, manifest the difference between negativity of the Wigner functions. The non-Gaussianity of these states is also examined and show that the difference in behavior of their non-Gaussianity is the same as the difference between negativity of their Wigner functions. We also investigate the influence of correlation rank criterion and find that when the states can be produced locally from classical states, the Wigner functions cannot reveal their quantum correlations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Revealing quantum correlation by negativity of the Wigner function

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1255-6
Publisher site
See Article on Publisher Site

Abstract

We analyze two two-mode continuous variable separable states with the same marginal states. We adopt the definition of classicality in the form of well-defined positive Wigner function describing the state and find that although the states possess positive local Wigner functions, they exhibit negative Wigner functions for the global states. Using the negativity of Wigner function as an indicator of nonclassicality, we show that despite these states possess different negativities of the Wigner function, they do not reveal this difference as phase space nonclassicalities such as negativity of the Mandel Q parameter or quadrature squeezing. We then concentrate on quantum correlation of these states and show that quantum discord and local quantum uncertainty, as two well-defined measures of quantum correlation, manifest the difference between negativity of the Wigner functions. The non-Gaussianity of these states is also examined and show that the difference in behavior of their non-Gaussianity is the same as the difference between negativity of their Wigner functions. We also investigate the influence of correlation rank criterion and find that when the states can be produced locally from classical states, the Wigner functions cannot reveal their quantum correlations.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 11, 2016

References

  • Density operators and quasiprobability distributions
    Cahill, KE; Glauber, RJ
  • Coherent and incoherent states of the radiation field
    Glauber, RJ
  • On the quantum correction for thermodynamic equilibrium
    Wigner, EP
  • Theory and application of the quantum phase-space distribution functions
    Lee, HW
  • When is the Wigner function of multidimensional systems nonnegative?
    Soto, F; Claverie, P
  • Mixed states with positive Wigner functions
    Bröcker, T; Werner, RF
  • Detecting quantum non-Gaussianity via the Wigner function
    Genoni, MG; Palma, ML; Tufarelli, T; Olivares, S; Kim, MS; Paris, MGA
  • Can quantum-mechanical description of physical reality be considered complete?
    Einstein, A; Podolsky, B; Rosen, N
  • Characterizing nonclassical correlations via local quantum uncertainty
    Girolami, D; Tufarelli, T; Adesso, G

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