Universal Super-Tensorization of Jensen–Shannon Divergence Contraction Coefficients

Universal strict super-tensorization of Jensen–Shannon divergence contraction coefficients. Note (2026). See the erratum to 10.5281/zenodo.18248854: channel-only contraction coefficients satisfy ηf(W) = ηχ2(W) for all f-divergences, so super-tensorization is not JSD-specific, and the contrast with multiplicative tensorization below conflates the channel-only and source-dependent definitions. Result. For every finite channel W with nontrivial contraction 0 < ηJSD(W) < 1, one has ηJSD(W⊗2) > 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. Method. The Ordentlich–Polyanskiy binary edge reduction expresses the binary JSD SDPI constant as a normalized posterior-variance functional; strict amplification follows from the law of total variance. The convergence rate is controlled by the Bhattacharyya coefficient: 1 − ηn(W) ≤ 2An. Numerical verification over 4729 random channels across 26 configurations confirms zero violations. Update v1.1. An addendum with three targeted clarifications: (1) precise assumptions for the binary edge reduction lemma, replacing the informal “mild regularity conditions”; (2) an explicit two-case split in the key strictness argument (Lemma 5.2, Step 2); (3) a refined table caption for operator-convex divergences.