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Register a new userA Measure of Non-Markovianity for Unital Quantum Dynamical Maps
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One of the most important topics in the study of the dynamics of open quantum system is information exchange between system and environment. Based on the features of a back-flow information from an environment to a system, an approach is provided to detect non-Markovianity for unital dynamical maps. The method takes advantage of non-contractive property of the von Neumann entropy under completely positive and trace preserving unital maps. Accordingly, for the dynamics of a single qubit as an open quantum system, the sign of the time-derivative of the density matrix eigenvalues of the system determines the non-Markovianity of unital quantum dynamical maps. The main characteristics of the measure is to make the corresponding calculations and optimization procedure simpler.
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We provide an analysis on non-Markovian quantum evolution based on the spectral properties of dynamical maps. We introduce the dynamical analog of entanglement witness to detect non-Markovianity and we illustrate its behaviour with several instructive examples. It is shown that for a certain class of dynamical maps the shape of the body of accessible states provides a simple non-Markovianity witness.
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We identify a set of dynamical maps of open quantum system, and refer to them as $ epsilon $-Markovian maps. It is constituted of maps which, in a higher dimensional system-environment Hilbert space, possibly violate Born approximation but only a little. We characterize the $epsilon$-nonmarkovianity of a general dynamical map by the minimum distance of that map from the set of $epsilon$-Markovian maps. We analytically derive an inequality which gives a bound on the $ epsilon$-nonmarkovianity of the dynamical map, in terms of an entanglement-like resource generated between the system and its immediate environment. In the special case of a vanishing $epsilon$, this inequality gives a relation between the $epsilon$-nonmarkovianity of the reduced dynamical map on the system and the entanglement generated between the system and its immediate environment. We numerically investigate the behavior of the similar distant based measures of non-Markovianity for classes of amplitude damping and phase damping channels.
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