  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.
