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Quantum Information Processing

The negativity of Wigner function as a measure of quantum correlations

Fatima-Zahra Siyouri, M. El Baz, Y. Hassouni

Published Jul 12, 2016• 40 citations
Publisher
DOI
10.1007/s11128-016-1380-2

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We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.
We study the dynamics of Wigner function, quantum discord, entanglement and quantum dissonance for bipartite Bell-diagonal states independently interacting with dephasing reservoirs. We analyze comparatively their behavior under the decoherence effect. Our main goal is to test the ability of Wigner function negativity to measure all kinds of quantum correlations in such system. Particularly, we find that this negativity can only capture entanglement and discord. Of course it succeeded in predicting the behavior of quantum dissonance, but nevertheless, it failed to detect its presence. As a matter of fact, we conclude that Wigner function negativity cannot be used as measure of quantum dissonance in the two qubit open system.
The presence of unique quantum correlations is the core of quantum-information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using correlation functions defined for quasiprobability distributions. In particular, we discuss the possibility of probing the negativity of a quasiprobability by comparing moments of the Wigner function. We show that one must take at least the fourth moments to find the negativity in general and the eighth moments for states with a rotationally invariant Wigner function.