Recoverability of quantum channels via hypothesis testing

Abstract

A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in arXiv:2208.12194, we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of $L_1$-distance.

arXiv comment13 pages, comments welcome. Extended from previous version to infinite dimensions

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Cited by in corpus (6)

• Quantum Rényi and $f$-divergences from integral representations
• Quantum Channel Learning
• Continuity of entropies via integral representations
• Entanglement cost for infinite-dimensional physical systems
• Optimising the relative entropy under semidefinite constraints
• Macroscopicity and observational deficit in states, operations, and correlations