Quantum channels with polytopic images and image additivity

Abstract

We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class. We then provide a complete characterization of quantum channels $T$ that are universally image additive in the sense that for any quantum channel $S$, the image of $T\otimes S$ is the convex hull of the tensor product of the images of $T$ and $S$. These channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical-quantum channels.

References in corpus (1)

• Hastings' additivity counterexample via Dvoretzky's theorem

Cited by in corpus (7)

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• Recoverability in quantum information theory
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• Random positive operator valued measures
• Entanglement-Saving Channels
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula