No-hypersignaling principle

TL;DR

This paper introduces the concept of hypersignaling, showing that quantum theory's characterization requires constraints on both space-like and time-like correlations, not just space-like correlations alone.

Contribution

It constructs a toy model demonstrating anomalous time-like correlations, highlighting the need for additional principles beyond space-like correlations to characterize quantum theory.

Findings

Toy model exhibits hypersignaling behavior in time-like correlations.

Space-like correlations alone do not distinguish quantum from certain non-quantum theories.

Constraints on time-like correlations are necessary to fully characterize quantum theory.

Abstract

A paramount topic in quantum foundations, rooted in the study of the EPR paradox and Bell inequalities, is that of characterizing quantum theory in terms of the space-like correlations it allows. Here we show that to focus only on space-like correlations is not enough: we explicitly construct a toy model theory that, while not contradicting classical and quantum theories at the level of space-like correlations, still displays an anomalous behavior in its time-like correlations. We call this anomaly, quantified in terms of a specific communication game, the "hypersignaling" phenomena. We hence conclude that the "principle of quantumness," if it exists, cannot be found in space-like correlations alone: nontrivial constraints need to be imposed also on time-like correlations, in order to exclude hypersignaling theories.