## 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.

### MSC:

 81P15 Quantum measurement theory, state operations, state preparations 81P16 Quantum state spaces, operational and probabilistic concepts 94A17 Measures of information, entropy 62F03 Parametric hypothesis testing 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
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