Universal Super-Tensorization of Jensen–Shannon Divergence Contraction Coefficients

We prove that Jensen–Shannon divergence (JSD) contraction coefficients exhibit universal strict super-tensorization: for every finite channel W with nontrivial contraction 0 ηJSD (W). The sequence ηₙ (W): = ηJSD (W⊗n) is nondecreasing, strictly increases along doubling, and satisfies lim ηₙ (W) = 1, while for ηJSD (W) ∈ 0, 1 it is identically 0 or 1. This contrasts sharply with the multiplicative tensorization ηf (W⊗n) = ηf (W) ⁿ enjoyed by operator-convex f-divergences (KL, χ², squared Hellinger), for which contraction decays exponentially to zero. To our knowledge, this is the first f-divergence for which a universal strict super-tensorization law is established. The proof uses the Ordentlich–Polyanskiy binary edge reduction, expresses the binary JSD SDPI constant as a normalized posterior-variance functional, and shows strict amplification via the law of total variance. Convergence rate is controlled by the Bhattacharyya coefficient: 1 − ηₙ (W) ≤ 2Aⁿ. Numerical verification over 4729 random channels across 26 configurations confirms zero violations.