A quantum channel is entanglement breaking exactly when its Choi state is a separable quantum state. If , the Choi reconstruction formula gives a measure-and-prepare channel with POVM . Conversely, applying an entanglement-breaking channel to a maximally entangled state produces a separable Choi state. Horodecki, Shor and Ruskai's entanglement-breaking channel paper develops the equivalences.
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