Monogamy relations for relativistically causal correlations

TL;DR

This paper derives entropic monogamy relations for relativistically causal correlations, showing that certain non-local constraints prevent superluminal signaling and challenge previous mechanisms proposed for such correlations.

Contribution

It introduces a general method to derive entropic monogamy relations for relativistically causal correlations, clarifying their non-local structure and implications.

Findings

Monogamy relations prevent superluminal signaling.

Relativistically causal correlations satisfy specific entropic inequalities.

Previous mechanisms for such correlations are refuted by these monogamy constraints.

Abstract

Non-signalling conditions encode minimal requirements that any (quantum) systems must satisfy in order to be consistent with special relativity. Recent works have argued that in scenarios involving more that two parties, correlations compatible with relativistic causality do not have to satisfy all possible non-signalling conditions but only a subset of them. Here we show that correlations satisfying only this subset of constraints have to satisfy highly non-local monogamy relations between the effects of space-like separated random variables. These monogamy relations take the form of entropic inequalities between the various systems and we give a general method to derive them. Using these monogamy relations we refute previous suggestions for physical mechanisms that could lead to relativistically causal correlations, demonstrating that such mechanisms would lead to superluminal signalling.