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Physica Scripta

Characterizing non-Markovian quantum evolution

Dariusz Chruściński

Published Mar 1, 2013• 0 citations
Publisher

Abstract

We analyze classes of legitimate quantum dynamics using a local in time master equation. Markovian dynamics is characterized in terms of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian quantum evolution. They are based on a simple observation that Markovian dynamics implies monotonic behavior of several well-known quantities such as distinguishability of states, fidelity and relative entropy.

DOI
10.1088/0031-8949/2013/t153/014009

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We analyze classes of legitimate quantum dynamics using a local in time master equation. Markovian dynamics is characterized in terms of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian quantum evolution. They are based on a simple observation that Markovian dynamics implies monotonic behavior of several well-known quantities such as distinguishability of states, fidelity and relative entropy.
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We construct a large class of completely positive and trace-preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics for statistical operators characterized by a continuous time evolution interrupted by jumps, randomly distributed in time and described by a quantum channel. The state of the open system is shown to obey a closed evolution equation, given by a master equation with a memory kernel and an inhomogeneous term. The non-Markovianity of the obtained dynamics is explicitly assessed studying the behavior of the distinguishability of two different initial system's states with elapsing time.
The study of non-Markovian quantum processes has attracted significant interest in recent decades, giving rise to several competing notions of quantum non-Markovianity. These notes serve as an introduction to the topic for graduate students familiar with quantum mechanics and probability theory. Owing to the vastness of the literature, we focus on two prominent characterizations of quantum Markovianity based on the divisibility of quantum channels and monotonically decreasing state distinguishability. The correspondence between classical concepts (stochastic matrices, Chapman-Kolmogorov equation) and their quantum analogs (dynamical maps, CP-divisibility) is emphasized throughout.