Extending the Known Region of Nonlocal Boxes that Collapse Communication Complexity

TL;DR

This paper identifies new conditions under which nonlocal boxes, theoretical models of correlations, can drastically simplify communication complexity, extending the known regions where such collapse is possible, thus providing insights into the limits of physical theories.

Contribution

It introduces a refined sufficient condition for nonlocal boxes to collapse communication complexity, expanding the known collapsing region within the space of non-signalling boxes.

Findings

New sufficient condition for collapse of communication complexity

Extension of the collapsing region beyond previous bounds

Identification of a region outside an ellipse where collapse occurs

Abstract

Non-signalling boxes (NS) are theoretical resources defined by the principle of no-faster-than-light communication. They generalize quantum correlations, and some of them are known to collapse communication complexity (CC). However, this collapse is strongly believed to be unachievable in Nature, so its study provides intuition on which theories are unrealistic. In the present letter, we find a better sufficient condition for a nonlocal box to collapse CC, thus extending the known collapsing region. In some slices of NS, we show this condition coincides with an area outside of an ellipse.