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

Key Points

• The aim is to explore the tensorization behavior of the Jensen–Shannon divergence contraction under specific channels.
• Derived an exact closed-form expression for the contraction coefficient in a two-fold product channel.
• Analyzed the convergence of contraction coefficients in blocklength for tensor powers.
• Identified the mechanism behind non-factorization of the midpoint distribution under product measures.
• Established strict super-tensorization of the Jensen–Shannon divergence contraction coefficient.
• Proved that contraction coefficients are nondecreasing as blocklength increases.
• Demonstrated the convergence of coefficients to one in the tensor powers context.