Maximal Non-Classicality in Multi-Setting Bell Inequalities

TL;DR

This paper investigates the relationship between quantum correlations and entanglement in multi-setting Bell inequalities, revealing different behaviors of entanglement entropy depending on the number of measurement settings.

Contribution

It provides analytical and numerical analysis of maximal quantum violations and the nature of most non-classical states in multi-setting Bell inequalities.

Findings

For N=2, entanglement entropy is monotone in d and the most non-classical state is not maximally entangled.

For N>2, entanglement entropy is non-monotone in d and approaches that of maximally entangled states as d increases.

Maximal quantum violations are characterized for various numbers of settings and outcomes.

Abstract

The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family Bell inequalities with $N$-settings and $d$ outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of $d$ and many measurement settings. Interestingly, we find that the entanglement entropy behaves very differently depending on whether $N=2$ or $N> 2$: when $N=2$ the entanglement entropy is a monotone function of $d$ and the most non-classical state is far from maximally entangled, whereas when $N> 2$ the entanglement entropy is a non-monotone function of $d$ and converges to that of the maximally entangled state in the limit of large $d$.