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Reversibility conditions for quantum operations. (English) Zbl 1254.81010
Summary: We give a list of equivalent conditions for reversibility of the adjoint of a unital Schwarz map, with respect to a set of quantum states. A large class of such conditions is given by preservation of distinguishability measures: $f$-divergences, $L_1$-distance, quantum Chernoff and Hoeffding distances. Here, we summarize and extend the known results. Moreover, we prove a number of conditions in terms of the properties of a quantum Radon-Nikodym derivative and factorization of states in the given set. Finally, we show that reversibility is equivalent to preservation of a large class of quantum Fisher informations and $\chi^2$-divergences.

81P15Quantum measurement theory
81P16Quantum state spaces, operational and probabilistic concepts
94A17Measures of information, entropy
62F03Parametric hypothesis testing
81-02Research monographs (quantum theory)
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