Revealing quantum correlation by negativity of the Wigner function

TL;DR

This paper investigates how negativity in the Wigner function can reveal quantum correlations in continuous variable states that appear classical locally, highlighting differences not captured by traditional nonclassicality measures.

Contribution

It demonstrates that Wigner function negativity can detect quantum correlations in states that are locally classical, and explores the role of non-Gaussianity and correlation criteria.

Findings

Negativity of the Wigner function indicates quantum correlations.

Local classical states can have globally negative Wigner functions.

Wigner negativity reveals quantum correlations not seen by Mandel Q or squeezing.

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 can not reveal their quantum correlations.