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System-environment correlations for dephasing two-qubit states coupled to thermal baths

A. C. S. Costa, M. W. Beims, and W. T. Strunz
Phys. Rev. A 93, 052316 – Published 12 May 2016
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  • INTRODUCTION
  • DILATING QUBIT DEPHASING
  • MODEL FOR SYSTEM AND ENVIRONMENT
  • TOTAL STATE DYNAMICS
  • NUMERICAL RESULTS FOR WERNER STATES
  • OTHER BIPARTITIONS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial X state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature Tcrit. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to Tcrit the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.

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    • Received 10 December 2015

    DOI:https://doi.org/10.1103/PhysRevA.93.052316

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Entanglement measuresNonlocalityOpen quantum systemsOpen quantum systems & decoherence
    Quantum Information, Science & TechnologyGeneral Physics

    Authors & Affiliations

    A. C. S. Costa1,2,*, M. W. Beims1,†, and W. T. Strunz2,‡

    • 1Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil
    • 2Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany

    • *ana.sprotte@gmail.com
    • †mbeims@fisica.ufpr.br
    • ‡walter.strunz@tu-dresden.de

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    Issue

    Vol. 93, Iss. 5 — May 2016

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    Images

    • Figure 1
      Figure 1

      Scheme of the proposed model. System of two qubits (AB) with qubit A coupled to the environment (E).

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    • Figure 2
      Figure 2

      Temperature-time diagram. Red (dark gray) region, entangled SE state; blue (light gray) region, separable SE state. Parameters are κ=10−3 (weak coupling) and c=0.2 (no initial entanglement between the two qubits). Remarkably, for kBTcrit≈0.13ℏωc, the total state oscillates as a function of time between separable and entangled regions.

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    • Figure 3
      Figure 3

      Temperature-time diagram. Red (dark gray) region, entangled SE state; blue (light gray) region, separable SE state. The black dashed line indicates the decoherence time scale and the black full line the two-qubit sudden death. While below the black full line the two-qubit system has some amount of entanglement, above this line the entanglement vanishes. Parameters are κ=10−3 (weak coupling) and (a) c=0.5 and (b) c=0.9 for kBTcrit≈0.16ℏωc in (a) and for kBTcrit≈0.29ℏωc in (b), the total state oscillates as a function of time between separable and entangled regions.

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    • Figure 4
      Figure 4

      Temperature-time diagram. Red (dark gray) region, entangled SE state; blue (light gray) region, separable SE state. Parameters are κ=1 (strong coupling) and c=0.2 (no initial entanglement between the two qubits). The black dashed line indicates the decoherence time scale

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    • Figure 5
      Figure 5

      Temperature-time diagram. Red (dark gray) region, entangled SE state; blue (light gray) region, separable SE state. The black dashed line indicates the decoherence time scale and the black full line the two-qubit sudden death. While below the black full line the two-qubit system has some amount of entanglement, above this line the entanglement vanishes. Parameters are κ=1 (strong coupling) and (a) c=0.5 and (b) c=0.9.

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    • Figure 6
      Figure 6

      Concurrence for weak coupling (κ=10−3), with c=0.5 and kBT=0.1ℏωc (black full line), kBT=0.2ℏωc (black dashed line), and kBT=0.3ℏωc (black dotted line). We can see oscillations of concurrence which gets smoothed out with increase of temperature.

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