Classical information capacity of a class of quantum channels

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  • 16 December 2004
Abstract
We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. This class is the one for which the norm of the output is maximized for an output state being a normalized projection. For such channels - which we characterize in their general form - we prove the additivity of the minimal output Renyi entropies with entropic parameters contained in [0, 2], generalizing an argument by Alicki and Fannes, and present several examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify instances of weakly covariant channels for which we can infer the additivity of the classical information capacity. Both additivity results apply to the case of an arbitrary number of different channels. Finally, we relate the obtained results to instances of bi-partite quantum states for which the entanglement cost can be calculated.

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