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arXiv:1205.5969 · Physical Review A

Dynamics of genuine multipartite correlations in open quantum systems

Arne L. Grimsmo, A. S. Parkins, Bo-Sture Skagerstam

Published Aug 8, 2012• 12 citations
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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.

DOI
10.1103/physreva.86.022310

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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.
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Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to determine the macroscopic behavior of the steady-state multipartite mutual information between N interacting units undergoing Markovian evolution that is invariant under unit permutations. Using this approach, we extend a conclusion previously drawn for classical systems that either the extensive scaling of mutual information is not possible for systems relaxing to fixed points of the mean-field dynamics, or such scaling is not robust to perturbations of system dynamics. In contrast, robust extensive scaling occurs for a system relaxing to time-dependent attractors, e.g., limit cycles. We illustrate the applicability of our method on the driven-dissipative Lipkin-Meshkov-Glick model.
Entanglement between two noninteracting particles can give rise to their joint motion. This suggests that entanglement may be a kind of resource to activate collective behavior in multipartite systems. However, here we argue that entanglement is neither a necessary nor a sufficient condition for a multipartite collective dynamics. We consider an NNN-partite scenario and show that a genuinely multipartite entangled noninteracting system can move collectively. Nevertheless, at the same time any MMM-partite (1<M<N1<M<N1<M<N) subsystem, which also moves collectively, is classically correlated. Moreover, since there is no interaction, such a subsystem would behave the same way if the remaining $N\ensuremath{-}M$ particles were removed. This proves that entanglement is not necessary for a collective motion. Next, we introduce external potentials and show that some collective dynamical properties cannot be observed unless an interaction between the particles is turned on.
In this paper, we present a measure of quantum correlation for a multipartite system, defined as the sum of the correlations for all possible partitions. Our measure can be defined for quantum discord (QD), geometric quantum discord or even for entanglement of formation (EOF). For tripartite pure states, we show that the multipartite measures for the QD and the EOF are equivalent, which allows direct comparison of the distribution and the robustness of these correlations in open quantum systems. We study dissipative dynamics for two distinct families of entanglement: a W state and a GHZ state. We show that, for the W state, the QD is more robust than the entanglement, while for the GHZ state, this is not true. It turns out that the initial genuine multipartite entanglement present in the GHZ state makes the EOF more robust than the QD.
We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.