Entanglement Evolution of Three-Qubit States under Local Decoherence

Wei Song, Da-Chuang Li, Zhuo‐Liang Cao

Xiao-San Ma, Liu Gao-Sheng, Wang An-Min

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.

Thiago Rodrigues de Oliveira

Exploring an analytical expression for the convex roof of the pure state squared concurrence for rank 2 mixed states the entanglement of a system of three particles under decoherence is studied, using the monogamy inequality for mixed states and the residual entanglement obtained from it. The monogamy inequality is investigated both for the concurrence and the negativity in the case of local independent phase damping channel acting on generalized Greenberger-Horne-Zeilinger states of three particles and the local independent amplitude damping channel acting on generalized $\ensuremath{\mid}\mathrm{W}⟩=\ensuremath{\mid}001⟩+\ensuremath{\mid}010⟩+\ensuremath{\mid}100⟩$ state of three particles. It is shown that the bipartite entanglement between one qubit and the rest has a qualitative similar behavior to the entanglement between individual qubits, and that the residual entanglement in terms of the negativity cannot be a good entanglement measure for mixed states, since it can increase under local decoherence.

Mohammad Mehdi Sahrapour, Nancy Makri

János K. Asbóth, Петер Адам, Mátyás Koniorczyk +1 more

DAN GAO, Zhao Zhen-Shuang, Hong‐Fu Wang +2 more

We investigate the effect of the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction on entanglement in a three-qubit Ising model with intrinsic decoherence. The entanglement of the nearest and the next-nearest neighbor qubit is calculated. The results show that, taking into account the intrinsic decoherence, when the qubits are initially in the maximal entangled state, the concurrence of the system decreases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t. When the qubits are initially in the disentangled state, the destructive effect of intrinsic decoherence on entanglement can be moderated by the Dzyaloshinskii–Moriya interaction, the concurrence increases with the increasing Dzyaloshinskii–Moriya interaction following the evolution of the time t.