Death to additivity?

I’m no expert on the additivity conjectures for quantum channels but it would appear that there may now exist a way of randomly choosing states which are not additive for the classical capacity of a quantum channel. If this paper is on the money (Matt Hastings’ papers normally are) then it looks like quantum channels may not be additive.

Oh, and as everyone knows that the quantum capacity of quantum channels was shown not to be additive a few months back by in this neat paper by Yard and Smith.

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2 thoughts on “Death to additivity?

  1. A minor comment: Hastings showed that a Holevo function is nonadditive, which means that capacity of a channel is not simply given by Holevo quantity maximized over a single channel use. So this is quite different type of result than that of Yard and Smith result, which tells that capacity itself is nonadditive.

    I.e. we still do not know, whether classical capacity of a quanutm channel is additive or not. Let me mention, that it was recently shown that quantum channels with two senders and one receiver can exhibit nonadditivity (Czekaj and Horodecki, arxiv.org).

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