Almost Quantum Correlations are Inconsistent with Specker's Principle

TL;DR

This paper demonstrates that almost quantum correlations cannot satisfy Specker's principle, challenging previous assumptions about the relationship between Specker's principle and quantum-like correlations.

Contribution

It proves that almost quantum correlations are incompatible with Specker's principle, providing a new criterion to distinguish quantum correlations from broader probabilistic theories.

Findings

Almost quantum correlations violate Specker's principle.

Specker's principle cannot be satisfied by theories producing almost quantum correlations.

The result narrows the space of theories compatible with Specker's principle.

Abstract

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (https://vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.