Generalized relative entropies and the capacity of classical-quantum channels

Abstract

We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeffding capacity, that we define similarly to the Holevo capacity, but replacing the relative entropy with the Hoeffding distance. Similarly, our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max-relative entropy in the definition of the divergence radius of a channel.

Published version

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• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Second-order asymptotics for quantum hypothesis testing
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• One-Shot Coherence Dilution
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• Semidefinite programming strong converse bounds for classical capacity
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• Applications of position-based coding to classical communication over quantum channels
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• Encoding classical information into quantum resources
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• Semantic Security for Quantum Wiretap Channels
• Universal random codes: Capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender
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