No-signaling, perfect bipartite dichotomic correlations and local randomness

TL;DR

This paper reviews no-signaling constraints, derives new inequalities to distinguish no-signaling correlations from general ones, and shows that perfect correlations imply local randomness under no-signaling, with potential cryptographic implications.

Contribution

It introduces a novel set of no-signaling inequalities resembling CHSH and demonstrates their implications for local randomness in perfect correlations.

Findings

New no-signaling inequalities close to CHSH are derived.

Existing inequalities by Roy, Singh, Avis are shown to be trivial.

Perfect correlations under no-signaling imply local randomness for identical devices.

Abstract

The no-signaling constraint on bi-partite correlations is reviewed. It is shown that in order to obtain non-trivial Bell-type inequalities that discern no-signaling correlations from more general ones, one must go beyond considering expectation values of products of observables only. A new set of nontrivial no-signaling inequalities is derived which have a remarkably close resemblance to the CHSH inequality, yet are fundamentally different. A set of inequalities by Roy and Singh and Avis et al., which is claimed to be useful for discerning no-signaling correlations, is shown to be trivially satisfied by any correlation whatsoever. Finally, using the set of newly derived no-signaling inequalities a result with potential cryptographic consequences is proven: if different parties use identical devices, then, once they have perfect correlations at spacelike separation between dichotomic observables, they know that because of no-signaling the local marginals cannot but be completely random.