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Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
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quant-phcs.ITmath.IT
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capacityquantumchannelsclassicalcapacitieschannelenvironment-assistedmixture
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The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.
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