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AIP conference proceedings

Time Evolution of Continuous Variable Entanglement in Open Quantum Systems

Аурелиан Исар, L. Trache, Alexei Smirnov, Sabin Stoica

Published Jan 1, 2010• 0 citations
Publisher

Abstract

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 of two‐mode Gaussian states, we describe the evolution of entanglement 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 a zero temperature the initial entangled state remains entangled for finite times. We also show that, independent of its type—separable or entangled, the initial state evolves asymptotically to an equilibrium state which is always separable.

DOI
10.1063/1.3527244

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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 of two‐mode Gaussian states, we describe the evolution of entanglement 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 a zero temperature the initial entangled state remains entangled for finite times. We also show that, independent of its type—separable or entangled, the initial state evolves asymptotically to an equilibrium state which is always separable.
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 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 uncoupled modes interacting with a thermal environment. Using Peres‐Simon necessary and sufficient criterion for separability of two‐mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse and revival of entanglement take place. We analyze also the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.
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.
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 uncoupled harmonic oscillators interacting with a thermal environment. Using Peres‐Simon necessary sufficient criterion for separability of two‐mode Gaussian states, we show that for some values of diffusion coefficient, dissipation constant and temperature of the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse revival of entanglement take place.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a repeated collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.
Using the theory of open systems based on completely positive quantum dynamical semigroups, we describe the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal reservoir. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type - separable or entangled. In other cases, entanglement generation, entanglement sudden death or a repeated collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of quantum entanglement.