Berry phase and quantum entanglement in Majorana's stellar representation
Berry phase and quantum entanglement in Majorana's stellar representation
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马约拉纳恒星表征中的贝里相和量子纠缠
DOI：
10.1103/physreva.94.022123
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发表时间：
2016-08-31
影响因子：
2.9
通讯作者：
Fu, L. B.
中科院分区：
文献类型：
--
作者：
Liu, H. D.;Fu, L. B.
通过用布洛赫球体上Majorana恒星的轨迹来呈现量子态的演化，Majorana的恒星为研究高维Hilbert空间的量子系统提供了直观的几何图像。我们通过这些恒星在Bloch球上的分布和运动来研究Berry位相和量子纠缠。结果表明，Majorana星可以很好地代表量子态的这两个独特性质。前者用马约拉纳星环的立体角和恒星之间的距离来表示。对于后者，恒星之间的距离也被发现是测量和分类对称多量子比特纯态的多粒子纠缠的工具。为了证明我们的理论，我们研究了一个典型的自旋模型，它等价于相互作用的玻色子模型或相互作用的多量子比特系统。内部的自陷现象也通过Majorana恒星进行了讨论。
By presenting the evolution of a quantum state with the trajectories of the Majorana stars on the Bloch sphere, the Majorana's stellar provides an intuitive geometric picture to study a quantum system with high-dimensional Hilbert space. We study the Berry phase and quantum entanglement by distributions and motions of these stars on the Bloch sphere. It is shown that both of these unique characters of quantum state can be perfectly represented by the Majorana stars. The former is expressed by the solid angles of Majorana star loops and the distance between stars. For the latter, the distances between stars are also found to be a tool for measuring and classifying the multiparticle entanglement of a symmetric multiqubit pure state. To demonstrate our theory, we study a typical spin model which is equivalent to an interacting boson model or an interacting multiqubit system. The self-trapping phenomenon within is also discussed via the Majorana stars.