Non-locality distillation and post-quantum theories with trivial communication complexity

TL;DR

This paper introduces an optimal protocol for distilling non-locality in post-quantum theories, showing that such non-local boxes trivialize communication complexity and are unlikely to exist naturally, providing insights into quantum non-locality limits.

Contribution

The authors present an optimal deterministic distillation protocol for correlated non-local boxes and demonstrate their trivialization of communication complexity, offering new understanding of quantum non-locality constraints.

Findings

All correlated non-local boxes can be distilled to maximally non-local boxes.

Distilled non-local boxes make communication complexity trivial.

Some non-local boxes are arbitrarily close to classical correlations.

Abstract

We first present a protocol for deterministically distilling non-locality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of post-quantum non-local boxes, which we term correlated non-local boxes. In the asymptotic limit, all correlated non-local boxes are distilled to the maximally non-local box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard \textit{et al.} [Phys. Rev. Lett. 96, 250401 (2006)] we show that all correlated non-local boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these non-local boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum non-locality is limited.