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International Journal of Modern Physics B

Role of Wigner function in studying quantum correlations

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

Published Sep 13, 2016• 5 citations
Publisher

Abstract

In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.

DOI
10.1142/s0217979216501873

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In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.
Abstract In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger–Horne–Zeilinger (GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation [Int. J. Mod. Phys. B 30 (2016) 1650187] may be generalized to the multipartite case.
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.
In this paper, we investigate comparatively the behaviors of quantum discord and concurrence for Werner states based on two bipartite entangled squeezed states. The maximally entangled squeezed states are regarded as a perfect-Werner states, while the non-maximally entangled squeezed states are called quasi-Werner states. We show that, the behavior of the quantum correlations keep unchanged for these two types of states. However, the quantum correlations amount presents in perfect-Werner states is very higher than that presents in quasi-Werner ones. Furthermore, we show that for large values of squeezed parameter the quasi-Werner states approaches the perfect-Werner states qualitatively and quantitatively.
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.
Abstract The significance of photon addition in engineering the single‐ and two‐mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, the behavior of the Wigner function of two quasi‐Werner states constructed by superposing two normalized bipartite m‐photon added coherent states are analyzed. This allows the authors' to quantify the nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured using concurrence, entanglement of formation, and quantum discord. The WLN for a two‐mode state corresponds to the sum of the single‐mode nonclassicality and quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi‐Werner states as quantum channel for the teleportation of single‐mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. The non‐Gaussian operation is shown effective in stalling the detrimental effects of transmission through noisy channel and/or inefficient detection under realistic scenario. Further, in contrast to a set of existing results, it is established that the negative values of two‐mode Wigner function is not a witness of quantum correlation.
Quantum correlations in a physical system are usually studied with respect to a unique and fixed decomposition of the system into subsystems, without fully exploiting the rich structure of the state space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness measures. Furthermore, we give a different perspective regarding how to reassess the fact that local operations play a key role in general quantumness measures that go beyond entanglement---as discordlike ones. We propose a family of measures to quantify the maximum quantumness of a given state. For the discord-based case, we present some analytical results for $2\ifmmode\times\else\texttimes\fi{}d$-dimensional states. Applying our definition to low-dimensional bipartite states, we show that different behaviors can be reported for separable and entangled states vis-\`a-vis those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Daki\ifmmode \acute{c}\else \'{c}\fi{}, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)].