On compression of non-classically correlated bit strings

TL;DR

This paper introduces a new information-theoretic approach to analyze non-classical correlations in bit strings, using compression rates and inequalities that distinguish classical from non-classical correlations, with implications for quantum mechanics.

Contribution

It proposes a novel method based on compression rates and inequalities to characterize non-classical correlations, extending the analysis beyond traditional approaches.

Findings

Classically correlated bit strings obey specific inequalities.

PR-boxes violate these inequalities.

Potential quantum violations are hypothesized.

Abstract

In this short note we present a new approach to non-classical correlations that is based on the compression rates for bit strings generated by Alice and Bob. We use normalised compression distance introduced by Cilibrasi and Vitanyi to derive information-theoretic inequalities that must be obeyed by classically correlated bit strings and that are violated by PR-boxes. We speculate about a violation of our inequalities by quantum mechanical correlations.