Dynamics of genuine multipartite correlations in open quantum systems

Abstract

We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to study an interacting collective system of atoms undergoing phase transitions as external parameters are varied. We show that the steady state of the system can have a significant degree of genuine multipartite quantum and classical correlations, and that the proposed measure can serve as a witness of critical behavior in quantum systems.PACS numbers: 03.65. Ud,03.67.Mn,05.70.Fh Introduction.-There is a lot of interest in the characterization and quantification of correlations between quantum systems. The fact that quantum systems can be correlated in ways that classical systems can not is generally understood to be essential to emerging quantum technologies [1], and thus understanding the nature of such correlations is one of the most active areas of research in quantum information theory. Recently, there has been much effort made towards quantifying correlations-quantum or classical-for multipartite (as opposed to bipartite) systems. In particular, there exists a question of whether or not a system contains genuine multipartite correlations, i.e., are there correlations that cannot be accounted for by any subsystem alone. A general framework, where a measure for a type of correlation was defined as the "distance", as measured by relative entropy, from one state with a defining property to the closest state without said property, was recently proposed by Modi et al. in [2]. This framework permits a unified view of the measures of relative entropy of entanglement [3], quantum discord [4], classical correlations [5], quantum mutual information and several new quantities. A powerful feature of this framework is that the suggested measures are well defined, and relations between them also hold for multipartite systems, thereby allowing for natural extensions of the above quantities beyond the bipartite case. A natural follow up to the work in [2] was done by Giorgi et al. in [6] where n-partite quantum and classical correlations were further divided into genuine and non-genuine parts. This is not the only effort in this direction however, and it is not known how to correctly measure genuine multipartite correlations. Investigations of the validity of the various measures involving the dynamical evolution of correlations in experimentally relevant situations therefore seem beneficial. This is the purpose of the work presented here.

Time evolution of tripartite quantum discord and entanglement under local and nonlocal random telegraph noise

“…Recently, a number of theoretical works examined the dynamics of non-classical correlations in tripartite sys- tems coupled to external environments characterized by different memory properties [6,[9][10][11][12][13]25]. While different approaches have been adopted to estimate entanglement [6,9,10,12,13] and Bell non-locality [11], few studies focus on the time evolution of tripartite quantum correlations in terms of quantum discord [25].…”

“…This implies that the suppression of the sudden death of entanglement cannot be detected while, as indicated by Eqs. (25), the long-time entanglement protection can successfully be revealed.…”

“…Under suitable conditions quantum discord is also found to be more robust than entanglement in noisy environments [17]. While the characterization of quantum discord in terms of the discrepancy between two quantum analogues of the classical mutual information has well been grasped and widely used in bipartite systems, its extensions in multipartite systems is still discussed and tackled with different approaches [22][23][24][25][26][27]. Recently, Giorgi et al [26] introduced a measure of genuine total, classical, and quantum correlations relying on the use of relative entropy to quantify the distance between two density matrices.…”

Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics

“…Gühne et al used the geometric measure of entanglement [32,33] to study the global dephasing process of four-qubit GHZ, cluster, W, and Dicke states [34]. Grimsmo et al used the entropic measure for average n-partite entanglement over quantum trajectories [35]. Gheorghiu and Gour developed the evolution of an averaged SL-invariant entanglement measure for local decoherence [36].…”

Average entanglement dynamics in open two-qubit systems with continuous monitoring

“…As a consequence, also the entanglement in the system vary according to how the environment is being monitored, and its time evolution can then be systematically characterized in an efficient way [18,19]. Numerical and analytical explorations of this proposal allowed for the description of the dynamics of entanglement [18][19][20][21] and entanglement of assistance [22] in various experimentally relevant situations, and preluded the formulation of new protocols for entanglement protection [23] and quantum computation [24], as well as its extension for the study of general quantum correlations [25]. Here we present a rigorous implementation of the quantum trajectory theory for the systematic study of the dynamics of entanglement in open quantum systems of two-qubits, and lay with clarity the groundwork for its extension to quantum systems of arbitrary size.…”