Classical information capacity of a class of quantum channels

Abstract

We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. 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 a number of 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 several 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.

14 pages, RevTeX (replaced with published version)

References in corpus (4)

• Complete hierarchies of efficient approximations to problems in entanglement theory
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Additivity properties of a Gaussian Channel
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p

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• Maximal output purity and capacity for asymmetric unital qudit channels
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• Simplification of additivity conjecture in quantum information theory
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• Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels
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• Tighter monogamy relations of multiqubit entanglement in terms of Rényi-$\alpha$ entanglement
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• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels
• An application of decomposable maps in proving multiplicativity of low dimensional maps