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理论物理通讯：英文版

Entanglement Dynamics of Multipartite Systems Under Decoherence from a Spin Environment

Xie, Guo-Qiu, Wang, An-Min, Ma, Xiao-San

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The entanglement evolution of multipartite quantum states under a spin environment is analyzed. Due to interaction, the extent to which the entanglement vanishes depends not only on the size of system and the structure of quantum states, but also on the exchange couplings with environment. The decoherence-free subspaces have been identified by using the linear entropy.

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Entanglement Dynamics of Multipartite Systems Under Decoherence from a Spin Environment

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We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.

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Entanglement sharing and decoherence in the spin-bath

Christopher M. Dawson, Andrew P. Hines, Ross H. McKenzie +1 more

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arXiv:quant-ph/0407206•Physical Review A•May 17, 2005•63 citations
The entanglement evolution of multipartite quantum states under a spin environment is analyzed. Due to interaction, the extent to which the entanglement vanishes depends not only on the size of system and the structure of quantum states, but also on the exchange couplings with environment. The decoherence-free subspaces have been identified by using the linear entropy.
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.
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.
The time evolution of genuine multipartite entanglement is numerically studied in a model many-spin system decohered by a structured spin bath. It is found that multipartite entanglement can be more persistent than the bipartite entanglement and can even evolve into a specific constant under certain conditions. Besides, multipartite entanglement sudden death and sudden birth are observed. It is shown that the randomness of the coupling strength and connectivity between the spins in the environment will suppress these birth and death phenomena. Furthermore, the initial state of the central system plays a significant role in determining multipartite entanglement dynamics.
We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.
The monogamous nature of entanglement has been illustrated by the derivation of entanglement-sharing inequalities---bounds on the amount of entanglement that can be shared among the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomenon in the spin-bath environment, constructing an entanglement-sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence.