Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy

By Mark M. Wilde, Andreas J. Winter, Dong Yang. Communications in Mathematical Physics, 2013

587 citations recorded by the source corpus.

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a “sandwiched” Rényi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/cb52c3918bef123ffaa2d29c07ca8a8868355a6a

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Citations in the corpus

Quantum Conditional Mutual Information and Approximate Markov Chains (2014, unknown): “Let Dα(·‖·) be the α-QuantumRényi Divergence as defined in [40,55].”
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “There are two non-commutative extensions of the notion of α−Rényi divergence [30, 54].”
Quantum Information Processing with Finite Resources - Mathematical Foundations (2015, background): “ion-theoretic arguments. A signiﬁcant part of this book is thus devoted to exploring quantum generalization of Renyi entropies, for example the´ ones proposed by Petz [116] and a more recent specimen [108,156] that has already found many applications. The particular problems encountered in cryptogra”