The essence of nonclassicality: non-vanishing signal deficit

TL;DR

This paper introduces a unified assumption linking communication cost and signaling to explain nonclassical properties of correlations, extending previous results to broader contexts including quantum temporal correlations.

Contribution

It generalizes nonclassicality results by deriving key properties from excess communication cost over signaling, relaxing the no-signaling condition.

Findings

Derived nonclassical properties from a single assumption

Extended nonlocal-nonsignaling correlation results

Generalized uncertainty bounds on nonlocality

Abstract

Nonclassical properties of correlations-- like unpredictability, no-cloning and uncertainty-- are known to follow from two assumptions: nonlocality and no-signaling. For two-input-two-output correlations, we derive these properties from a single, unified assumption: namely, the excess of the communication cost over the signaling in the correlation. This is relevant to quantum temporal correlations, resources to simulate quantum correlations and extensions of quantum mechanics. We generalize in the context of such correlations the nonclassicality result for nonlocal-nonsignaling correlations (Masanes, Acin and Gisin, 2006) and the uncertainty bound on nonlocality (Oppenheim and Wehner, 2010), when the no-signaling condition is relaxed.