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理论物理通讯：英文版

Bipartite and Tripartite Entanglement in a Three-Qubit Heisenberg Model

Ren, Jie Jie, Zhu, Shi-Qunt

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

在有一个不一致的磁场的 three-qubit Heisenberg XYmodel 的由两部组成、分成三部分的纠纷被学习。当磁场的振幅在三 qubits 之间是不同地分布式的时，在由两部组成的纠纷的同时发生有二或四座山峰。当磁场的振幅被改变时，注意没有在三 qubits 之间的分成三部分的纠纷的混乱很有趣。然而，磁场方向的变化能导致混乱。混乱关于在磁场和旋转的 z 轴之间的角度是周期的。

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Bipartite entanglement in spin-1/2 Heisenberg model

胡明安, 田东平

Chinese Physics C•Jan 1, 2008•0 citations
在有一个不一致的磁场的 three-qubit Heisenberg XYmodel 的由两部组成、分成三部分的纠纷被学习。当磁场的振幅在三 qubits 之间是不同地分布式的时，在由两部组成的纠纷的同时发生有二或四座山峰。当磁场的振幅被改变时，注意没有在三 qubits 之间的分成三部分的纠纷的混乱很有趣。然而，磁场方向的变化能导致混乱。混乱关于在磁场和旋转的 z 轴之间的角度是周期的。
本文利用绝热近似方法和精确对角化方法研究三量子比特Dicke模型中的纠缠动力学. 处于两种典型的纠缠态GHZ态和W态上的量子比特在时间演化过程中与辐射光场发生强耦合作用, 在各种子系统间产生纠缠, 通过分析这些纠缠的演化特性发现初始GHZ态的三体纠缠鲁棒性比W态强, 这与旋波近似结论一致. 与旋波近似下结果不同的是, 两种态中任意一对量子比特间的纠缠都随时间演化到几乎为零, 而三体纠缠随时间周期演化, 且纠缠程度相对较强, 说明系统中的强耦合作用通过抑制量子比特中的对纠缠来支持三体纠缠.
The bipartite and tripartite entanglement in a three-qubit Heisenberg XY model with a nonuniform magnetic field is studied. There are two or four peaks in the concurrence of the bipartite entanglement when the amplitudes of the magnetic fields are differently distributed between the three qubits. It is very interesting to note that there is no tangle of tripartite entanglement between the three qubits when the amplitudes of the magnetic fields are varied. However, the variation of the magnetic field direction can induce the tangle. The tangle is periodic about the angle between the magnetic field and the z axis of the spin.
The spatial distribution of entanglement within a spin-1/2 Heisenberg star composed from a single central spin and three peripheral spins is examined in the presence of an external magnetic field using the Kambe projection method, which allows an exact calculation of the bipartite and tripartite negativity serving as a measure of the bipartite and tripartite entanglement. Apart from a fully separable polarized ground state emergent at high-enough magnetic fields, the spin-1/2 Heisenberg star exhibits at lower magnetic fields three outstanding nonseparable ground states. The first quantum ground state exhibits the bipartite and tripartite entanglement over all possible decompositions of the spin star into any pair or triad of spins, whereby the bipartite and tripartite entanglement between the central and peripheral spins dominates over that between the peripheral spins. The second quantum ground state has a remarkably strong tripartite entanglement between any triad of spins in spite of the lack of bipartite entanglement. The central spin of the spin star is separable from the remaining three peripheral spins within the third quantum ground state, where the peripheral spins are subject to the strongest tripartite entanglement arising from a two-fold degenerate W-state.
We investigate bipartite and tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We adapt a systematic approach in calculating the entanglement of various bipartite splits usinga generalized concurrence as an indicator of entanglement. Our calculations are based on a direct detection scheme that is a particular unravelling of the density matrix. This system has a collective dipole-dipole energy shift that couples the atoms and the dissipation is via partially collective spontaneous emission described by the Lehmberg-Agarwal master equation.Our results are unravelling dependent, but apply to applications of entanglement based on direct detection. We also calculate the three-way tangle or residual entanglement for this system. We present calculations for a variety of driving and damping rates, and examine what decay rate is adequate for the system to be reduced to two qubits with a readout port. We also consider a specific model of three atoms located at particular positions in free space.