Comparative Study of Entanglement and Wigner Function for Multi-Qubit GHZ-Squeezed State

Fatima-Zahra Siyouri

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.

Antoine Royer

Jun Song, Hong-Yi Fan

Mario Arnolfo Ciampini, Todd Tilma, M. J. Everitt +4 more

Assessing the quality of a multi-qubit state is a multi-faceted problem, It involves considering disparate aspects, and, while some of these are collective indicators such as purity and degree of entanglement, others look more in detail at the form of the correlations between subsystems. Obtaining a visualisation of these details would give at least a qualitative indication, but the density matrix, with its large number of parameters, hardly offers insights. Here we show how relying on the Wigner function of a multipartite system provides rich information on the state, both at an illustrative level, by choosing proper slicing on the phase space, and at a quantitative one, by introducing new figures of merit for the state quality. We test this concept on a GHZ and W state produced in a photonic architecture making use of the multiple degrees of freedom of two photons.

Chunfeng Wu, Jing‐Ling Chen, L. C. Kwek +2 more

We construct an explicit Wigner function for the $N$-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the nonlocality of the multipartite entangled state by the violation of the \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski-Brukner $N$-qubit Bell inequality. We find that quantum predictions for such a squeezed state violate these inequalities by an amount that grows with the number $N$.

J. K. Sharma