= Binary test for quantum decoding success
{title2=$F_0=\sum_m|m\rangle\langle m|\otimes E_m$}
For $k$ equiprobable quantum code states decoded by a <POVM> $\{E_m\}$, testing whether the classical message label agrees with the decoded output gives a joint binary <POVM> with $F_0=\sum_m|m\rangle\langle m|\otimes E_m$. Its acceptance probability is the decoding success $1-\epsilon$ on the joint <classical-quantum state> and $1/k$ on the product of its marginals. Applying <quantum relative entropy> monotonicity to this test gives the <one-shot classical-quantum coding converse>.
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