Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement

TL;DR

This paper derives new analytical bounds linking the maximal violation of Bell inequalities to entanglement measures like negativity and concurrence for bipartite quantum states, enhancing understanding of nonlocality and entanglement relations.

Contribution

It introduces a novel upper bound on Bell inequality violations based on Schmidt coefficients and establishes the first general analytical relations between nonlocality and entanglement measures.

Findings

New upper bound on Bell violation using Schmidt coefficients

Analytical relations between Bell violation and negativity

Application to bipartite coherent states

Abstract

For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, J. Math. Phys. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities by a pure bipartite state, possibly infinite-dimensional, we derive a new upper bound expressed in terms of the Schmidt coefficients of this state. This new upper bound allows us also to specify general analytical relations between the maximal violation of Bell inequalities by a bipartite quantum state, pure or mixed, and such entanglement measures for this state as "negativity" and "concurrence". To our knowledge, no any general analytical relations between measures for bipartite nonlocality and entanglement have been reported in the literature though, for a general bipartite state, specifically such relations are important for the entanglement certification and quantification scenarios. As an example, we apply our new results to finding upper bounds on nonlocality of bipartite coherent states intensively discussed last years in the literature in view of their experimental implementations.