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arXiv:1307.1405 · Physical Review E

Signatures of chaos in the dynamics of quantum discord

Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, Shohini Ghose

Published Mar 10, 2015• 40 citations
arXivHTMLPDF

Abstract

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.

DOI
10.1103/physreve.91.032906

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We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.
Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose identify signatures of chaos in the dynamics of (e) discord in a multiqubit system collectively modelled as (eb) a quantum kicked top. Evolution of discord between any two qubits is (eb) quasiperiodic in regular regions, while (e) in chaotic regions the quasiperiodicity is (eb) lost. As the initial wave function is varied from (e) the regular regions to the chaotic sea, a contour plot of (e) the time-averaged discord remarkably reproduces (eb) the structures of the classical stroboscopic map. Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose also find surprisingly opposite behavior of (e) two-qubit discord versus entanglement of (e) the two qubits as measured by (e&eb) the concurrence. Results provide (eb) evidence of signatures of chaos in (eb).... The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-470888-475368.pdf
Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. Evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-405514-409887.pdf
We study the quantum signatures of chaos by using the concept of bipartite fluctuations in the kicked two-site Bose-Hubbard model, which can be mapped to the well-studied kicked top model. We find that the evolution of bipartite fluctuations is quasiperiodic when the initial state centered in the regular regions, while it becomes irregular as the initial state centered in the chaotic regions. As a result, the quantum signatures of chaos can be identified in both the dynamical bipartite fluctuations and the long time averaged bipartite fluctuations. We further demonstrate that the regular versus irregular behaviors of bipartite fluctuations are induced by the different localization properties of the evolved state in regular and chaotic regimes. Finally, we discuss how to identify the signature of global chaos via bipartite fluctuations; and point out the relationship between bipartite fluctuations and the classical Lyapunov exponent.
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. We find an increase in the rate of information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. The last part of this thesis is devoted to the study of the nature of quantum correlations themselves. We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information.
We investigate the dissipative dynamics of quantum discord in a decoherence model with two initially entangled qubits in addition to a quantum kicked top. The two qubits are uncoupled during the period of our study and one of them interacts with the quantum kicked top. We find that the long-time behavior of quantum discord could be well described by the fidelity decay of the quantum kicked top; for short-time behavior, however, the phase of the amplitude of the fidelity decay is necessary to provide more specific information about the system. We have made a comparison between the quantum kicked top and the multi-mode oscillator system in describing the environment, and also compared the dynamics of the entanglement with that of quantum discord.
We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.