Optimal state pairs for non-Markovian quantum dynamics

Abstract

We study a recently proposed measure for the quantification of quantum non-Markovianity in the dynamics of open systems which is based on the exchange of information between the open system and its environment. This measure relates the degree of memory effects to certain optimal initial state pairs featuring a maximal flow of information from the environment back to the open system. We rigorously prove that the states of these optimal pairs must lie on the boundary of the space of physical states and that they must be orthogonal. This implies that quantum memory effects are maximal for states which are initially distinguishable with certainty, having a maximal information content. Moreover, we construct an explicit example which demonstrates that optimal quantum states need not be pure states.

6 pages, 2 figures

References in corpus (4)

• Assessing non-Markovian dynamics
• Non-Markovian quantum jumps
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Quantum Semi-Markov Processes

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• Non-Markovian qubit dynamics in a circuit-QED setup
• Determining the squeezing in multimode fields using nonlocal quantum probes
• Bounds for the divisibility-based and distinguishability-based non-Markovianity measures
• Efficient Scheme of Experimental Quantifying non-Markovianity in High-Dimension Systems