Non-Markovianity through Accessible Information

Abstract

The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behavior of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment. The inevitable interaction between a system and its environment typically results in the loss of quantum features, such as coherence [1,2]. One important aspect in the study of these so-called open quantum systems is the concept of non-Markovianity, which arises due to memory effects of the environment. Non-Markovian features might enable the system to recover part of the lost coherence and information back from the environment [1][2][3][4]. Although these memory effects have been investigated in the past, only recently an increase in the understanding of nonMarkovianity from a quantum information perspective has emerged [5][6][7][8][9][10][11].The non-Markovian nature of a dynamical quantum map can be characterized through a number of distinct methods [5][6][7][8][9][10]. To date, the measure defined by Breuer, Laine, and Piilo [6] based on trace distance, is the most significant quantifier of the degree of non-Markovianity, due to its interpretation: non-Markovianity manifests itself as a reverse flow of information from the environment back to the system. An alternative method to measure the degree of non-Markovianity relies on the fact that local, completely positive trace-preserving (CPTP) maps cannot increase the entanglement between an open quantum system and an isolated ancillary system [12]. Exploiting this property, Rivas, Huelga, and Plenio (RHP) have defined another measure for the degree of non-Markovianity [7]. According to the RHP measure, a dynamical process is said to be nonMarkovian if the entanglement between the open system and the isolated ancilla temporarily increases throughout the dynamics. Although the RHP measure provides a connection between the non-Markovian behavior of dynamical maps and entanglement, a meaning in terms of information flow is still lacking in this approach.Here, we propose an entanglement-based measure of non-Markovianity having a direct information based interpretation. Our method is based on the decoherence program [13], where a system S is coupled to a measurement ...

Distributed correlations and information flows within a hybrid multipartite quantum-classical system

“…1 can be described by the standard decoherence paradigm of a quantum system (qubit A) quantum correlated with a measurement apparatus (qubit B) which in turn interacts with an environment (E) [41] and looking for the flows of information between the system A and the environment E [42,43]. Here we are interested in comprehending the mechanisms which give rise to the revivals of two-qubit entanglement by approaching the problem from an information-theoretic point of view.…”

Time-invariant discord in dynamically decoupled systems

“…Thus, similarly to DD techniques, non-Markovianity can also be used to restore monotonically decaying correlations [10]. An ongoing debate concerns itself with characterizing and quantifying non-Markovianity [11][12][13][14][15][16][17][18][19]. At present, no universal measure exists and indeed in some cases, connections between measures can not be established [20,21].…”

Characterizing non-Markovianity via quantum interferometric power

“…Among the most important ones, let us mention those based on the deviation of the dynamical maps from divisible CPTP maps [6,7] and those based on the nonmonotonicity of the trace distance or distinguishability [8], entanglement [6], quantum mutual information [28], and channel capacities [18]. Other significant attempts to quantify non-Markovianity include the flow of quantum Fisher information [29], fidelity between dynamical time-evolved states [30], distinguishability in Gaussian quantum systems in terms of fidelity [31], volume of Gaussian states [32], backflow via accessible information [33], and local quantum uncertainty [34]. Recent proposals have also been made to characterize non-Markovianity in direct analogy to entanglement theory [35] and to study the links between system-environment quantum correlations and non-Markovian behavior [36].…”