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arXiv quant-ph/0511034quant-ph
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纠缠双比特态的拓扑相位和SO(3)群的表示

Topological phase for entangled two-qubit states and the representation of the SO(3)group

F. De Zela

摘要:

讨论了$SO(3)$群的两比特最大纠缠态(MES)表示.我们分析了$SO(3)$和实验上可实现的双量子位MES之间的对应关系。因此,我们提供了一个新的解释最近提出的一些实验的基础上MES。利用量子光学的工具,我们用双量子位微扰理论处理了中子干涉测量中的一些经典实验,这些实验表明自旋$1/2$粒子在磁场中进动产生了$π$相。通过这样做,我们可以分析最近提出的实验--以及未来的同类实验--与过去进行的实验相比,将在多大程度上涉及新的物理方面。我们认为,所提出的实验确实扩展了显示$SO(3)$的双重连通性的可能性,尽管对于这种情况,结果有必要将$SU(2)$的元素映射到作用于两级系统的物理操作上。

英文摘要:

We discuss the representation of the $SO(3)$ group by two-qubit maximally entangled states (MES). We analyze the correspondence between $SO(3)$ and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the $π$-phase accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of $SO(3)$, although for that to be the case it results necessary to map elements of $SU(2)$ onto physical operations acting on two-level systems.

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