We investigate the non-Markovian behavior in open quantum systems from an information-theoretic perspective. Our main tool is the max-relative entropy, which quantifies the maximum probability with which a state ρ can appear in a convex decomposition of a state σ . This operational interpretation provides a new view for the non-Markovian process. We also find that max-relative entropy can be the witness and measure of non-Markovian processes. As applications, some examples are also given and compared with other measures in this paper.
We investigate the non-Markovian behavior in open quantum systems from an information-theoretic perspective. Our main tool is the max-relative entropy, which quantifies the maximum probability with which a state ρ can appear in a convex decomposition of a state σ . This operational interpretation provides a new view for the non-Markovian process. We also find that max-relative entropy can be the witness and measure of non-Markovian processes. As applications, some examples are also given and compared with other measures in this paper.
Abstract We propose an alternative non-Markovianity measure of open quantum systems, which is based on max-information. The max-information is a one-shot generalization of the mutual information derived from the max-relative entropy. This operational interpretation provides a new site for viewing the non-Markovian process. As applications, some typical noisy channels have been investigated: for phase damping and amplitude damping channels, non-Markovianity measure based on max-information is equivalent to the three previous non-Markovianity measures, i.e. the measures based on the distinguishability, entanglement of environment and the mutual information. For the random unitary channel, the proposed measurement in the witness of Markovianity is equivalent to the measures based on quantum trace distance and thus overlaps partly with the measurement based on the mutual information. It shows that max-information may be a better candidate for correlation-based measurement of non-Markovian than the mutual information.
Abstract The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the quantum-incoherent relative entropy of coherence ( QI QI REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the QI QI REC. Also we implement an all-optical experiment to demonstrate that the behavior of the QI QI REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, both theoretically and experimentally, we show that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the QI QI REC and the phenomenon of information backflow. Our methods for detecting non-Markovianity are applicable to general quantum evolutions.
Abstract Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e. the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on l 1 norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative entropy of coherence are more comfortable than the original Tsallis relative entropy of coherence for small .
Entropy, and its temporal evolution, play a central role in the foundations of quantum theory and in modern quantum technologies. Here we study, in particular, the relations between the --- in general, non-Markovian --- evolution of an open quantum system, the notions of divisibility of a dynamical map and of distinguishability of quantum states, and the temporal behaviour of various entropy-related quantities such as the Renyi (and sandwiched Renyi) divergences, and the so-called min- and max- conditional entropies. This, in turn, gives rise to an operational meaning of (non-)Markovianity.
Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.
In the study of open quantum systems, memory effects are usually ignored, and this leads to dynamical semigroups and Markovian dynamics. However, in practice, non-Markovian dynamics is the rule rather than the exception. With the recent emergence of quantum information theory, there is a flurry of investigations of non-Markovian dynamics, and several significant measures for non-Markovianity are introduced from various perspectives such as deviation from divisibility, information exchange between a system and its environment, or entanglement with the environment. In this work, by exploiting the correlations flow between a system and an arbitrary ancillary, we propose a considerably intuitive measure for non-Markovianity by use of correlations as quantified by the quantum mutual information rather than entanglement. The fundamental properties, physical significance, and differences and relations with existing measures for non-Markovianity are elucidated. The measure captures quite directly and deeply the characteristics of non-Markovianity from the perspective of information. A simplified version based on Jamio\l{}kowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization is also proposed.