Remark: Non-product is not synonymous with transmissive

The constant channel $\rho \mapsto |{\Phi }^{+}⟩⟨{\Phi }^{+}{|}_{PQ}\mathrm{Tr}\rho$ has a non-product output but transmits no input dependence in either direction. Transmission must be established by an operational witness or a failure of reduced-channel factorization, not by block diameter or non-product structure alone.