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Recoverability of quantum channels via hypothesis testing
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Recoverability of quantum channels via hypothesis testing
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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.
Forward citations
Cited by 3 Pith papers
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Integral representations of $f$-divergences for general von Neumann algebras
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
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Semidefinite optimization yields arbitrarily tight upper and lower bounds on the quantum relative entropy of channels via discretized linearization of an integral representation.
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Quantum hockey stick f-divergences are extended to general von Neumann algebras, with regularized Rényi versions shown to coincide with standard Petz and sandwiched Rényi divergences.
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