Elemental and tight monogamy relations in nonsignalling theories

TL;DR

This paper establishes stronger monogamy relations for nonsignalling correlations, showing how nonlocality constrains any correlations among parties and improving protocols for quantum key distribution and randomness amplification.

Contribution

It introduces tighter monogamy relations for nonsignalling correlations, extending the understanding of nonlocality constraints beyond Bell violations.

Findings

Stronger monogamy bounds for nonsignalling correlations.

Limits on external knowledge about measurement outcomes.

Enhanced protocols for quantum key distribution and randomness amplification.

Abstract

Physical principles constrain the way nonlocal correlations can be distributed among distant parties. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed among a set of parties by the violation observed by a different set of parties. We prove here that much stronger monogamy relations are possible for nonsignalling correlations by showing how nonlocal correlations among a set of parties limit any form of correlations, not necessarily nonlocal, shared among other parties. In particular, we provide tight bounds between the violation of a family of Bell inequalities among an arbitrary number of parties and the knowledge an external observer can gain about outcomes of any single measurement performed by the parties. Finally, we show how the obtained monogamy relations offer an improvement over the existing protocols for device-independent quantum key distribution and randomness amplification.