Why Super-Quantum, Non-Signaling Correlations Cannot Exist

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.