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arXiv:1511.06788 · Physical Review A

Non-Markovianity through multipartite correlation measures

F. M. de Paula, Paola Concha Obando, M. S. Sarandy

Published Apr 26, 2016• 11 citations
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Abstract

We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum, classical, and total correlations can be used to quantify the degree of non-Markovianity of a local quantum decohering process. We illustrate our results by considering the dynamical behavior of the trace-distance correlations in multiqubit systems under local dephasing and generalized amplitude damping.

DOI
10.1103/physreva.93.042337

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We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum, classical, and total correlations can be used to quantify the degree of non-Markovianity of a local quantum decohering process. We illustrate our results by considering the dynamical behavior of the trace-distance correlations in multiqubit systems under local dephasing and generalized amplitude damping.
Abstract In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.
We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change in distinguishability. We study along the way the properties of leaked information, which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for the nonlocal memory effect.
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.
We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signaling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows us to shed light on the origin of non-Markovian behaviors in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavor and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain.