Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions
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There are different inequivalent ways to define the Rényi mutual information between the input and the output of a channel. In a 1995 paper Csiszár has shown that for classical discrete memoryless channels there is a distinguished such quantity that has an operational interpretation as a generalized cutoff rate for constant composition channel coding. We show that the analogous notion of Rényi mutual information, defined in terms of the sandwiched quantum Rényi divergences, has the same operational interpretation in the strong converse problem of classical-quantum channel coding. Denoting the constant composition strong converse exponent for a memoryless classical-quantum channel W with composition P and rate R as sc(W,R,P), our result is that sc(W,R,P)=_α>1α-1/α[R-χ_α,2^*(W,P)], whereχ_α,2^*(W,P) is the Augustin type sandwiched Rényi mutual information between the classical input and the quantum output of the channel for a given input distribution P.
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