Why Super-Quantum, Non-Signaling Correlations Cannot Exist

TL;DR

This paper demonstrates that super-quantum, non-signaling correlations cannot exist because physically realizable no-signaling systems must be described using quantum-like operator language, which enforces the Tsirelson bound.

Contribution

It clarifies the misconception that stronger-than-quantum no-signaling correlations can exist by showing they require a quantum-like operator framework, leading to the Tsirelson bound.

Findings

Super-quantum correlations are incompatible with quantum operator formalism.

No-signaling systems involving incompatible observables are described by non-commutative operators.

The Tsirelson bound naturally arises from the quantum-like description, ruling out stronger correlations.

Abstract

The idea that non-local correlations stronger than quantum correlations between two no-signaling systems could theoretically exist is based on an incorrect statistical interpretation of the no-signaling condition. This article shows that any physically realizable no-signaling box involving local incompatible observables indeed requires to be described in a non-commutative, quantum-like language of operators -which leads to the derivation of the Tsirelson bound and then contradicts this idea.