Reversibility conditions for quantum operations

Abstract

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 with preservation of a large class of quantum Fisher informations and χ^2-divergences.

27 pages, version accepted in Rev. Math. Phys. Proof of Lemma 9 changed, some explanations added, typos corrected

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• On superactivation of zero-error capacities and reversibility of a quantum channel
• Quantum $f$-divergences in von Neumann algebras I. Standard $f$-divergences
• Data processing for the sandwiched Rényi divergence: a condition for equality
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• A new quantum version of f-divergence
• Asymptotics of quantum Markov processes: From algebraic structure to characterization of asymptotic states
• Recoverability of quantum channels via hypothesis testing
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• Spectral Properties of Tensor Products of Channels
• Covariant quantum combinatorics with applications to zero-error communication
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• Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications
• Non-Markovianity in the Adapted Caldeira-Leggett model
• Characterization of linear maps on $M_n$ whose multiplicity maps have maximal norm, with an application in quantum information
• On singular Bosonic linear channels
• Compactness criterion for families of quantum operations in the strong convergence topology and its applications
• On equalities in two entropic inequalities
• Exact and local compression of quantum bipartite states
• Quantum detailed balance via elementary transitions