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Chinese Physics B

Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment

Shan Chuan-Jia, Tao Chen, Ji-Bing Liu, Cheng Wei-Wen, Tang-Kun Liu, Huang Yan-Xia, Hong Li

Published Jun 1, 2010• 7 citations
Publisher

Abstract

In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.

DOI
10.1088/1674-1056/19/6/060303

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In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
In this paper, we consider the entanglement dynamics of two cavities interacting with independent reservoirs. When the cavity entanglement suddenly disappeared, the reservoir entanglement suddenly and necessarily appears. We study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. Also, we find that the conditions on the apparition of the entanglement sudden death and the entanglement sudden birth can be generalized when the initial entangled state of cavities is not pure, which is a complement to the result in the paper [Phys. Rev. Lett.101 (2008) 080503] for the pure case.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms with initial X state and dipole-dipole coupling intensity in Tavis-Cummings model. The interesting phenomena of entanglement sudden death as well as sudden birth appear during the evolution process. We analyze in detail the effect of purity of initially entangled state of two atoms, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions for the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. The results show that the above system parameters affect the concurrence, entanglement sudden birth and sudden death remarkably, the dipole-dipole coupling intensity affects amplitudes of the concurrence oscillation and leads time interval of the ESD to decrease. With the increasing of the purity, the time of entanglement sudden death and entanglement sudden birth will decrease, it is also notable that invariant and stable entanglement, which can be controlled by different initial states of the atoms, occurs for particular initial X state.
In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.