Bell inequalities with no quantum violation and unextendible product bases

TL;DR

This paper explores Bell inequalities that are not violated by quantum mechanics but can be surpassed by supraquantum correlations, using bound entangled states derived from unextendible product bases.

Contribution

It identifies a class of bound entangled states from UPBs where quantum correlations do not outperform classical ones, yet supraquantum correlations can.

Findings

Quantum correlations do not violate certain Bell inequalities.

Supraquantum nonsignalling correlations can outperform quantum correlations.

Bound entangled states from UPBs exhibit these properties.

Abstract

The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases (UPBs) with a wide family of tasks, for which (i) quantum correlations do not outperform the classical ones but (ii) there exist supraquantum nonsignalling correlations that do provide an advantage.