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International Journal of Quantum Information

ENTANGLEMENT DYNAMICS OF THREE-QUBIT STATES UNDER A SPIN ENVIRONMENT

XIAO SAN MA, Gao Sheng Liu, An Min Wang

Published Mar 1, 2011• 3 citations
Publisher

Abstract

In this paper, we investigate the entanglement dynamics of three-qubit states under a spin environment. From the analysis, we find that the entanglement dynamics of the three-qubit states depends not only on the coupling strength between the system and the environment and the number of degrees of freedom of the environment but also on the tunneling matrix elements of the spin environment and the specific state of concern. Specifically, the entanglement dynamics of the GHZ state, the W state, and the Werner state have been analyzed in detail and the conditions to identify the decoherence-free subspaces of our model have been discussed.

DOI
10.1142/s0219749911006739

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In this paper, we investigate the entanglement dynamics of three-qubit states under a spin environment. From the analysis, we find that the entanglement dynamics of the three-qubit states depends not only on the coupling strength between the system and the environment and the number of degrees of freedom of the environment but also on the tunneling matrix elements of the spin environment and the specific state of concern. Specifically, the entanglement dynamics of the GHZ state, the W state, and the Werner state have been analyzed in detail and the conditions to identify the decoherence-free subspaces of our model have been discussed.
By using negativity as entanglement measure, we have investigated the effect of local decoherence from a non-Markovian environment on the time evolution of entanglement of three-qubit states including the GHZ state, the W state, and the Werner state. From the results, we find that the entanglement dynamics depends not only on the coupling strengths but also on the specific states of concern. Specifically, the entanglement takes different behaviors under weak or strong coupling and it varies with the quantum states under study. The entanglement of the GHZ state and the Werner state can be destroyed completely by the local decoherence, while the entanglement of the W state can survive through the local decoherence partially.
We investigate the entanglement dynamics of three-qubit states in a quantum-critical environment, which is an Ising model in a transverse field. By using negativity as entanglement measure, we find that the entanglement evolution depends not only on the system-environment couplings and the size of degrees of freedom of environment but also on the strength of transverse field and the symmetry of quantum states of concern. In particular, for the cases under study, our results imply that the entanglement decay can be enhanced by the quantum phase transition of the environment under weak coupling. Our analysis implies that the entanglement of any three-qubit quantum state will be completely destroyed by the decoherence under certain conditions, that we detail below.
In this paper, we have investigated the quantum entanglement of quantum states undergoing decoherence from a spin environment which drives a quantum phase transition. From our analysis, we find that the entanglement dynamics depends not only on the coupling strength but also on the external magnetic field and the number of the freedom degrees of the environment. Specially, our results imply that the decay of the entanglement can be enhanced by the quantum phase transition of the environment when the system is coupled to the environment weakly. Additionally, the discussion of the case of the multipartite states with high dimensions is made.
We investigate the entanglement dynamics of a two-qubit system which interacts with a Heisenberg XYXYXY spin chain constrained to carry an energy current. We show an explicit connection between the decoherence factor and entanglement, and numerically and analytically study the dynamical process of entanglement in both weak- and strong-coupling cases for two initial states, the general pure state and the mixed Werner state. We provide results that the entanglement evolution depends not only on the energy current, the anisotropy parameter and the system-environment couplings but also on the size of degrees of freedom of environment. In particular, our results imply that entanglement will be strongly suppressed by the introduction of energy current on the environmental spin chain in the weak-coupling region while it is not sensitive to the energy current in the strong-coupling region. We also observe the sudden death of entanglement in the system and show how the energy current affects the phenomenon.