Time reversals of irreversible quantum maps

Abstract

We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability to observe a transition between two states under the forward and the time reversed dynamics, and leads, as in the classical case, to fluctuation relations as tautological identities. As in classical dynamics in contact with a heat bath, time reversal is not unique, and we discuss several possibilities. For any bistochastic map its dual map preserves the trace and describes a legitimate dynamics reversed in time, in that case the entropy production in the environment vanishes. For a generic stochastic map we construct a simple quantum operation which can be interpreted as a time reversal. For instance, the decaying channel, which sends the excited state into the ground state with a certain probability, can be reversed into the channel transforming the ground state into the excited state with the same probability.

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References in corpus (4)

• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Fluctuation Relations for Diffusion Processes
• Quantum Operation Time Reversal
• Nonequilibrium potential and fluctuation theorems for quantum maps

Cited by in corpus (15)

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• Qubit noise deconvolution
• Quantum detailed balance conditions and fluctuation relations for thermalizing quantum dynamics
• Quasi inversion of qubit channels
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• Construction of propagators for divisible dynamical maps
• Fluctuation relation for heat exchange in Markovian open quantum systems
• Symmetry-induced fluctuation relations in open quantum systems
• Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics
• Detailed balance as a quantum-group symmetry of Kraus operators
• A perspective on Lindblad's Non-Equilibrium Entropy