= Memoryless quantum channel
{title2=$\Phi^{\otimes n}$}
A memoryless quantum channel has independent identical noise on successive uses, described by the tensor-power map $\Phi^{\otimes n}$. This factorization does not restrict the encoder to product inputs: one can feed an <entangled state> across uses. A block code with equally likely messages $m$ chooses states $\rho_m$ and a decoder <POVM> $(D_m)$. Its average error is $1-|\mathcal M|^{-1}\sum_m\operatorname{Tr}[D_m\Phi^{\otimes n}(\rho_m)]$, and its rate is $n^{-1}\log_2|\mathcal M|$. The <classical capacity of a quantum channel> allows such entangled block inputs; the one-use <Holevo capacity> gives the product-input capacity and requires regularization in general.
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