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Physical Review B

Entanglement evolution of three-qubit states in a quantum-critical environment

XIAO SAN MA, An Min Wang, Ya Cao

Published Oct 26, 2007• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.76.155327

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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.
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.
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 study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of the critical point of the environmental system.
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.
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.
In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.