Bell's Inequality, Generalized Concurrence and Entanglement in Qubits

TL;DR

This paper extends the relationship between Bell's inequality violation and entanglement, specifically generalized concurrence, to multi-qubit systems and demonstrates its application in topological models.

Contribution

It introduces a generalized relation between Bell's violation and concurrence for n-qubit states, expanding the understanding of quantum entanglement measures.

Findings

Upper bound of Bell's violation expressed as a function of generalized concurrence

Relation applied to Wen-Plaquette model to extract topological entanglement entropy

Extension of Bell-inequality entanglement relation to multi-qubit states

Abstract

It is well known that the maximal violation of the Bell's inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an $n$-qubit state has not been found. In the paper, we demonstrate some extensions of the relation between the upper bound of the Bell's violation and a {\it generalized} concurrence in several $n$-qubit states. In particular, we show the upper bound of the Bell's violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell's violation.