Super-Tensorization of Jensen–Shannon Divergence Contraction for the Binary Symmetric Channel

This work studies the tensorization behavior of the strong data-processing inequality (SDPI) contraction coefficient for the Jensen–Shannon divergence.For the binary symmetric channel BSC(δ), an exact closed-form expression is derived for the two-fold product channel, showing strict super-tensorization. It is further proved that the contraction coefficients for tensor powers are nondecreasing in blocklength and converge to one. The underlying mechanism is identified as the non-factorization of the midpoint distribution under product measures.