Quantum Nonlocality of Arbitrary Dimensional Bipartite States

TL;DR

This paper investigates the nonlocality of bipartite quantum states across various dimensions by deriving bounds on Bell inequality violations, improving detection methods for quantum nonlocality.

Contribution

It introduces a new analytical lower bound for nonlocality detection applicable to arbitrary bipartite states, extending previous results to higher dimensions.

Findings

Derived a computable lower bound for two-qubit states.

Showed the bound outperforms CHSH inequality in some cases.

Generalized the results to high-dimensional quantum states.

Abstract

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented.