Quantum Correlation Efficiency: Tsirelson's Bound from Čencov's Uniqueness Theorem via the Explaining-Away Penalty

Derives Tsirelson's bound (CHSH ≤ 2√2) from Čencov's uniqueness theorem via a new mechanism: quantum mechanics maximizes correlation efficiency S/I(D;M|Y), where I(D;M|Y) is the explaining-away penalty forced by the Fisher metric. Computational experiments across (N,2,2) Bell scenarios (N=2–8) show quantum's efficiency advantage diverges as N^2.54 (R²=0.9997). The quantum set is the unique efficiency frontier of information geometry.