Tsirelson's Bound

Tsirelson's bound (also written Cirel'son's bound) is the maximum degree to which quantum entanglement can violate Bell inequalities. Proved by Boris Tsirelson in 1980, it establishes that quantum correlations are strictly stronger than anything permitted by local realism, but strictly weaker than the maximum allowed by the no-signaling principle alone. This gap — between quantum correlations and the maximum non-signaling correlations — is the most precise formal statement of what distinguishes quantum mechanics from both classical and hypothetical post-quantum theories. It is not a bound we chose; it is a bound the world enforces, and no one has a satisfying explanation for why.