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arXiv:1005.4224 · Physical Review A

Quantum-to-classical transition and entanglement sudden death in Gaussian states under local-heat-bath dynamics

Sandeep K. Goyal, Sibasish Ghosh A

Published Oct 29, 2010• 14 citations
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Abstract

Entanglement sudden death (ESD) in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterization of classicality in Gaussian states, the time to ESD is calculated by analyzing the covariance matrices of the system. The results for the two-mode system at $T=0$ and $T>0$ for the two types of bath states are generalized to $n$ modes, and are shown to be similar in nature to the results for the general discrete $n$-qubit system.

DOI
10.1103/physreva.82.042337

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Entanglement sudden death (ESD) in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterization of classicality in Gaussian states, the time to ESD is calculated by analyzing the covariance matrices of the system. The results for the two-mode system at T=0T=0T=0 and T>0T>0T>0 for the two types of bath states are generalized to nnn modes, and are shown to be similar in nature to the results for the general discrete nnn-qubit system.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we present a description of continuous-variable entanglement for a system consisting of two non-interacting modes embedded in a thermal environment. By using the Peres–Simon necessary and sufficient criterion for the separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for zero temperature of the thermal bath, the initial entangled state remains entangled for finite times. We also show that, independent of its type, namely separable or entangled, the initial state evolves asymptotically to an equilibrium state that is always separable.
In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two noninteracting modes embedded in a thermal environment. By using the Peres-Simon necessary and sufficient criterion for separability, we show that for all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath, the initial entangled state remains entangled for finite times. We analyze also the time evolution of logarithmic negativity, which characterizes the degree of entanglement of the state, and of Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement.
Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.
Manipulation of sudden death of entanglement (ESD) of two qubits interacting with statistically uncorrelated thermal reservoirs is investigated. It is shown that for initially prepared X-states of the two qubits a simple (necessary and sufficient) criterion for ESD can be derived with the help of the Peres-Horodecki criterion. This criterion implies that, in contrast to the zero-temperature case, at finite temperature of at least one of the reservoirs all initially prepared two-qubit X-states exhibit ESD. General conditions are derived under which ESD can be hastened, delayed, or averted.