论文标题
SU的量子步行（1,1）
Quantum walk for SU(1,1)
论文作者
论文摘要
我们提出了一个计划，以在相位空间中实施SU（1,1）的量子步行，该方案将与Heisenberg-Weyl组相关的量子概括。 SU（1,1）相干状态所描述的助行器的运动可以在双曲线或庞加莱磁盘上可视化。在一模式和两模式实现中，我们介绍了SU（1,1）组的相应的弹芯和条件转移运算符，他们与Heisenberg-Weyl组的关系进行了分析。概率分布，标准偏差和冯·诺伊曼熵用于描述步行过程。 SU（1,1）相干状态的非正交性排除了SU（1,1）的量子步行（1,1）。但是，可以通过增加巴格曼指数$ k $来降低不同的SU（1,1）相干状态之间的重叠，这表明两种模式实现提供了更多可能的模拟理想量子步行的可能性。
We propose a scheme to implement the quantum walk for SU(1,1) in the phase space, which generalizes those associated with the Heisenberg-Weyl group. The movement of the walker described by the SU(1,1) coherent states can be visualized on the hyperboloid or the Poincaré disk. In both one-mode and two-mode realizations, we introduce the corresponding coin-flip and conditional-shift operators for the SU(1,1) group, whose relations with those for Heisenberg-Weyl group are analyzed. The probability distribution, standard deviation and the von Neumann entropy are employed to describe the walking process. The nonorthogonality of the SU(1,1) coherent states precludes the quantum walk for SU(1,1) from the idealized one. However, the overlap between different SU(1,1) coherent states can be reduced by increasing the Bargmann index $k$, which indicates that the two-mode realization provides more possibilities to simulate the idealized quantum walk.
