= Rank-one Kraus representation of an entanglement-breaking channel
An <entanglement-breaking channel> admits a <Kraus representation> with rank-one <Kraus operators> $K_j=|a_j\rangle\langle b_j|$. Its <Choi state> is a sum of positive <tensor-product operators>, hence separable. Conversely, spectral decompositions of each prepared state and each <POVM> effect in a <measure-and-prepare channel> produce rank-one Kraus operators. Trace preservation imposes $\sum_j\lVert a_j\rVert^2|b_j\rangle\langle b_j|=I$.
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