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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
44/2020

Characterizing multipartite entanglement by violation of CHSH inequalities

Ming Li, Hui-Hui Qin, Chengjie Zhang, Shu-Qian Shen, Shao-Ming Fei and Heng Fan

Abstract

Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here, we consider the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show that the concurrence of a pure state in any high-dimensional multipartite system can be equivalently represented by these overlaps. Here, we consider the projections of an arbitrary high-dimensional multipartite state to two-qubit states. We investigate 1 the non-localities of these projected two-qubit sub-states by their violations of CHSH inequalities. From these violations, the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequality, we show that the concurrence of a high-dimensional multipartite pure state can be exactly expressed by these overlaps. We further derive a lower bound of the concurrence for any quantum states, which is tight for pure states. The lower bound not only imposes restriction on the non-locality distributions among the pairwise-qubit states, but also supplies a sufficient condition for distillation of bipartite entanglement. Effective criteria for detecting genuine tripartite entanglement and the lower bound of concurrence for genuine tripartite entanglement are also presented based on such non-localities.

Received:
Mar 17, 2020
Published:
Apr 1, 2020

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inJournal
2020 Repository Open Access
Ming Li, Huihui Qin, Chengjie Zhang, Shu-Qian Shen, Shao-Ming Fei and Heng Fan

Characterizing multipartite entanglement by violation of CHSH inequalities

In: Quantum information processing, 19 (2020) 5, p. 142