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Decoherence in time evolution of bound entanglement

Sun, Z, Gao, Y B, Sun, C P, Wang, X

Published Jan 15, 2007• 10 citations
OpenAlex

Abstract

We study a dynamic process of disentanglement by considering the time evolution of bound entanglement for a quantum open system, two qutrits coupling to a common environment. Here, the initial quantum correlations of the two qutrits are characterized by the bound entanglement. In order to show the universality of the role of environment on bound entanglement, both bosonic and spin environments are considered. We found that the bound entanglement displays collapses and revivals, and it can be stable against small temperature and time change. The thermal fluctuation effects on bound entanglement are also considered.

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We study a dynamic process of disentanglement by considering the time evolution of bound entanglement for a quantum open system, two qutrits coupling to a common environment. Here, the initial quantum correlations of the two qutrits are characterized by the bound entanglement. In order to show the universality of the role of environment on bound entanglement, both bosonic and spin environments are considered. We found that the bound entanglement displays collapses and revivals, and it can be stable against small temperature and time change. The thermal fluctuation effects on bound entanglement are also considered.
The effect of stochastic dephasing on the dynamics of entanglement of qutrit-qutrit states is investigated by using negativity and bound entanglement defined with realignment criterion. From the analysis, we find that the time evolution of quantum free entanglement and bound entanglement depends on the fluctuations of the stochastic variables and the parameters of the particular initial states of concern. Our results imply that some qutrits states display both distillability sudden death and entanglement sudden death, while some states do not display distillability sudden death but only entanglement sudden death.
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.
The exact reduced dynamics for two independent qudits dephasingly coupled to a common zero-temperature, super-Ohmic, bosonic environment is studied. It is shown that the qudit-qudit subsystem initially prepared in a separable state evolves into an entangled state. Details of the entanglement origination depend on both the coupling strength and the spectral properties of the environment as well as on the dimension of the qudit; the environment-induced entanglement can survive in the long-time limit. The entanglement dynamics of initially maximally entangled qudit-qudit states is analyzed for two examples: the qubit-qubit and qutrit-qutrit systems. The theory is applied to negative partial transposition entangled states of a two-qutrit system, which are shown to be distillable (for the assumed initial state) for arbitrary environment parameters.
We provide a detailed analysis of the time-evolutions of free and bound entangled states in a two-qutrit system under the effects of local/non-local classical dephasing noises. Namely the Ornstein-Uhlenbeck (OU) and the static noise are considered. The importance of the initial state is also analyzed by considering two completely different initially entangled states and their respective locally equivalent states by means of local unitary operation (LUO). The qutrits isotropic and bound entangled states are studied and we analyze their dynamical evolution to infer quantum states transition in the system. We demonstrate the absence of state transitions for isotropic-like states, unlike bound entangled-like states where free entangled states may lose distillability. Disentanglement however occurs for independents environments no matter the initial state. Meanwhile, for a common environment we show that indefinite free entanglement survival can be achieved (suppression of distillability sudden death) by converting the initial state using the LUO, hence saving free entanglement in the bipartite high dimensional quantum system, useful for quantum information and processing purposes.
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 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.