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Quantum Information and Computation

Quantum fidelity evolution of Penning trap coherent states in an asymmetric open quantum system

Somayeh Mehrabankar, Davood Afshar, Mojtaba Jafarpour

Published May 1, 2019• 0 citations
Publisher

Abstract

Assuming the Born-Markov approximation, we study the evolution of quantum fidelity in asymmetric systems consisting of two and three-mode independent oscillators interacting with a thermal bath. To this end, considering the Penning trap coherent states as the initial states of the system, we have studied the evolution of the quantum fidelity as a function of the parameters of the system, the environment and the initial state, in the framework of open systems theory. It is observed that fidelity is a decreasing function of the temperature and dissipation coefficient for both two and three-mode states. However, for the two-mode state, the fidelity is an oscillating function of time but a decreasing one in the low values of the magnetic field. In the case of a three-mode state, although the fidelity decreases with the magnetic field, dissipation coefficient and temperature, it is an irregular function of the asymmetric coefficient.

DOI
10.26421/qic19.5-6-3

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Assuming the Born-Markov approximation, we study the evolution of quantum fidelity in asymmetric systems consisting of two and three-mode independent oscillators interacting with a thermal bath. To this end, considering the Penning trap coherent states as the initial states of the system, we have studied the evolution of the quantum fidelity as a function of the parameters of the system, the environment and the initial state, in the framework of open systems theory. It is observed that fidelity is a decreasing function of the temperature and dissipation coefficient for both two and three-mode states. However, for the two-mode state, the fidelity is an oscillating function of time but a decreasing one in the low values of the magnetic field. In the case of a three-mode state, although the fidelity decreases with the magnetic field, dissipation coefficient and temperature, it is an irregular function of the asymmetric coefficient.
We describe the time evolution of the quantum coherence in an open system consisting of two coupled bosonic modes embedded in a thermal reservoir. We discuss the influence of the environment in terms of the covariance matrix for initial squeezed thermal states. The coherence is quantified using the relative entropy as a measure, and its dynamics is studied in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that the evolution of the quantum coherence strongly depends on the initial state of the system (squeezing parameter and thermal photon numbers), the parameters characterizing the thermal reservoir (temperature and dissipation coefficient) and the intensity of the coupling between the two modes.
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 study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain 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, entanglement sudden death or a periodic 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.
We describe the evolution of the quantum entanglement of an open system consisting of two bosonic modes interacting with a common thermal environment, described by two different models. The initial state of the system is taken of Gaussian form. In the case of a thermal bath, characterized by temperature and dissipation constant which correspond to an asymptotic Gibbs state of the system, we show that for a zero temperature of the thermal bath an initial entangled Gaussian state remains entangled for all finite times. For an entangled initial squeezed thermal state, the phenomenon of entanglement sudden death takes place and we calculate the survival time of entanglement. For the second model of the environment, corresponding to a non-Gibbs asymptotic state, we study the possibility of generating entanglement. We show that the generation of the entanglement between two uncoupled bosonic modes is possible only for definite values of the temperature and dissipation constant, which characterize the thermal environment.
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 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.
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.