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In discussing the classical capacity of quantum channels, as e.g. mentioned in Wilde's book (see section 20.6), it is possible that using entanglement at the encoder stage can improve transmission rate. In this regards, Wilde discusses a construction given in (Hastings 2009). This seems to rely on considering random mixed-unitary channels, and showing that the corresponding minimum output entropy is non-additive.

Are there other known examples of channels where entanglement at the encoder improves communication rates? Or any sort of more general understanding of some property the channel must have for this to be the case? I'd appreciate both source and explicit examples, if sufficiently simple ones are known.

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  • $\begingroup$ Just today, Mark Wilde mentioned the existence of an explicit example of such a channel as an open problem on Twitter. $\endgroup$
    – user19323
    Commented Aug 19, 2022 at 14:30
  • $\begingroup$ @ZBZ ah! I had no idea, thanks for the pointer. Hilarious coincidence. Guess these things are less understood than I thought $\endgroup$
    – glS ♦
    Commented Aug 19, 2022 at 14:51

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