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Dynamics of the entanglement rate in the presence of decoherence

Yi, X X, Cui, H T, Wang, X G

Published May 24, 2003• 3 citations
OpenAlex

Abstract

The dynamics of the entanglement rate are investigated in this paper for pairwise interaction and two special sets of initial states. The results show that for the given interaction and the decoherence scheme, the competitions between decohering and entangling lead to two different results--some initial states may be used to prepare entanglement while the others do not. A criterion on decohering and entangling is also presented and discussed.

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The dynamics of the entanglement rate are investigated in this paper for pairwise interaction and two special sets of initial states. The results show that for the given interaction and the decoherence scheme, the competitions between decohering and entangling lead to two different results--some initial states may be used to prepare entanglement while the others do not. A criterion on decohering and entangling is also presented and discussed.
Considering the dynamics of a two-qubit entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence. We find that for different decoherence models, there exists some special class of entangled states of which the pairwise entanglement is the most stable. The lifetime of the entanglement in these states is larger than other states with the same initial entanglement. In addition, we also investigate the dynamics of pairwise entanglement in the ground state of spin models such as Heisenberg and XXYXXYXXY models.
Ising model is the simplest Heisenberg model,research on the entanglement of this model will promote the development of solid quantum computer.Considering the phase decoherence of system,this paper investigates the entanglement dynamics of two qubits Ising chain with the DM interaction.It is found that the effects of phase decoherence and DM interaction on entanglement are dependent on the initial state of system.For some initial states,the entanglement of system is invariable.For some others,with the increase of time,the entanglement of system oscillates and decreases.In addition,increasing the DM interaction will decrease the entanglement and the oscillation period;increasing the phase decoherence rate will also decrease the entanglement,however,the oscillation period is unchanging.
We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important classes of multipartite entangled states, the Greenberger-Horne-Zeilinger and the W\mathit{W}W state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the W\mathit{W}W state, consistent with previous studies.
We investigate quantum decoherence of the multi-photon entangled state |ψ Nm ⟩ = m [cos γ| N − m ⟩ 1 | m ⟩ 2 + e i θ m sin γ| m ⟩ 1 | N − m ⟩ 2 ]. When the entangled channel |ψ Nm ⟩ is embedded in an environment, the channel decoheres and becomes a mixed state governed by a master equation. We calculate the linear entropy and the relative entropy of entanglement, which describe the mixedness and the amount of entanglement for the mixed state, respectively. We show that quantum decoherence weakens the amount of entanglement and enhances the mixedness with the time evolution. It is indicated that the relative entropy of entanglement depends on not only the initial entanglement angle and the decohering parameter, but also the number of photons in each mode. In particular, we find that the decohering speed depends on the number-difference of photons in the two modes. The larger the number-difference of photons is, the higher the decohering speed.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.