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Is there a notion of approximate entanglement breaking (EB) channels? Say, e.g. the output is always close to a separable state. If so, do the nice properties of the EB channels, such as additive classical capacity, carry over to the approximate case? (On a related note, approximate degradability has been studied in the literature.)

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This work (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.012332) may be relevant to your question. The authors have shown that "approximate additivity" holds for "approximately entanglement-breaking channels."

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    Commented Nov 9, 2023 at 16:02
  • $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ Commented Nov 9, 2023 at 16:02

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