New assessment on the nonlocality of correlation boxes

TL;DR

This paper reevaluates the nonlocality of correlation boxes using an alternative measure, revealing that some boxes are less nonlocal than quantum states in one measure but more in another, challenging previous assumptions.

Contribution

It introduces a new perspective on nonlocality measures and identifies correlation boxes with contrasting nonlocality properties across different inequalities.

Findings

Correlation boxes can be less nonlocal than quantum states under certain measures.

Some correlation boxes are more nonlocal than quantum states with respect to the 3322 inequality.

The choice of nonlocality measure significantly affects the perceived strength of nonlocal correlations.

Abstract

Correlation boxes are hypothetical systems capable of producing the maximal algebraic violation of Bell inequalities, beyond the quantum bound and without superluminal signaling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states has been regarded as a demonstration that the former are more nonlocal than the latter. By employing an alternative, consistent measure of nonlocality, we show that this conclusion is not necessarily true. In addition, we find a class of correlation boxes that are less nonlocal than the quantum singlet with respect to the Clauser-Horne-Shimony-Holt inequality, being, at the same time, more nonlocal with respect to the 3322 inequality.