Jenčová, Anna Reversibility conditions for quantum operations. (English) Zbl 1254.81010 Rev. Math. Phys. 24, No. 7, 1250016, 26 p. (2012). 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. Cited in 10 Documents 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 Keywords:2-positive maps; Schwarz maps; reversibility; \(f\)-divergences; Radon-Nikodym derivative; hypothesis testing; quantum Fisher information PDF BibTeX XML Cite \textit{A. Jenčová}, Rev. Math. Phys. 24, No. 7, 1250016, 26 p. (2012; Zbl 1254.81010) Full Text: DOI arXiv OpenURL References: [1] DOI: 10.1016/0022-1236(82)90022-2 · Zbl 0483.46043 [2] DOI: 10.1007/s00220-008-0417-5 · Zbl 1175.81036 [3] DOI: 10.1007/978-1-4612-0653-8 [4] DOI: 10.1103/PhysRevA.82.062306 [5] DOI: 10.1063/1.2186925 · Zbl 1111.47022 [6] Hayashi M., Quantum Information: An Introduction (2006) [7] DOI: 10.1103/PhysRevA.76.062301 [8] DOI: 10.1007/s00220-004-1049-z · Zbl 1126.82004 [9] Helstrom C. W., Quantum Detection and Estimation Theory (1976) · Zbl 1332.81011 [10] DOI: 10.1063/1.2872276 · Zbl 1153.81376 [11] DOI: 10.1142/S0129055X11004412 · Zbl 1230.81007 [12] DOI: 10.1137/1123048 · Zbl 0426.62085 [13] Jenčová A., Comm. Math. Phys. 263 pp 259276– [14] DOI: 10.1142/S0219025706002408 · Zbl 1108.46045 [15] DOI: 10.1007/s11005-010-0398-0 · Zbl 1201.46059 [16] DOI: 10.1142/S0129055X10004144 · Zbl 1218.81025 [17] DOI: 10.1063/1.3516474 · Zbl 1314.81123 [18] Jenčová A., Acta Sci. Math. (Szeged) 76 pp 27– [19] DOI: 10.1016/S0001-8708(74)80004-6 · Zbl 0274.46045 [20] DOI: 10.1007/s11005-004-4072-2 · Zbl 1055.81012 [21] Ohya M., Quantum Entropy and Its Use (2004) [22] Paulsen V., Completely Bounded Maps and Operator Algebras (2002) · Zbl 1029.47003 [23] DOI: 10.1093/qmath/35.4.475 · Zbl 0571.46042 [24] DOI: 10.1007/BF01212345 · Zbl 0597.46067 [25] Petz D., Rep. Math. Phys. 21 pp 57– [26] Petz D., Quart. J. Math. Oxford 39 pp 907– [27] DOI: 10.1016/0024-3795(94)00211-8 · Zbl 0856.15023 [28] DOI: 10.1063/1.3511335 · Zbl 1314.81124 [29] DOI: 10.1515/9783110850826 · Zbl 0594.62017 [30] DOI: 10.1016/0022-1236(72)90004-3 · Zbl 0245.46089 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.