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arXiv:quant-ph/0602045 · Journal of Physics A Mathematical and General

Entangling oscillators through environment noise

F Benatti, Roberto Floreanini B

Published Mar 1, 2006• 105 citations
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Abstract

We consider two independent bosonic oscillators immersed in a common bath, evolving in time with a completely positive, Markovian, quasi-free (Gaussian) reduced dynamics. We show that an initially separated Gaussian state can become entangled as a result of a purely noisy mechanism. In certain cases, the dissipative dynamics allows the persistence of these bath induced quantum correlations even in the asymptotic equilibrium state.

DOI
10.1088/0305-4470/39/11/009

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We consider two independent bosonic oscillators immersed in a common bath, evolving in time with a completely positive, Markovian, quasi-free (Gaussian) reduced dynamics. We show that an initially separated Gaussian state can become entangled as a result of a purely noisy mechanism. In certain cases, the dissipative dynamics allows the persistence of these bath induced quantum correlations even in the asymptotic equilibrium state.
In the framework of the theory of open systems based on quantum dynamical semigroups, we solve the master equation for two independent bosonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment and evolving under a Markovian, completely positive dynamics become asymptotically entangled for certain environments, so that their non-local quantum correlations exist in the long-time regime.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuousvariable entanglement for a system consisting of two independent harmonic oscillators interacting with a general 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 an arbitrary Gaussian input state.For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled.In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement.We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable.We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
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