论文标题
非自动两相量子步行的光谱分析在一个维度上
Spectral Analysis of Non-unitary Two-phase Quantum Walks in One Dimension
论文作者
论文摘要
最近，Asahara-funakawa-Seki-Tanaka表明，现有的chirally对称（离散时间）量子步行的索引理论可以扩展到非自利量子步行的设置。更确切地说，他们将两阶段拆分量子步行的某种非单身变体视为一个具体的一维示例，并在其研究中对相关指数进行了完整的分类。但是，请注意，与统一量子步行的设置不同，其指数是否给出了所谓拓扑受保护的结合状态数量的下限。实际上，非单身运算符的频谱可以是复杂平面的任何子集，因此在非单身情况下，这种结合状态的定义是模棱两可的。本文的目的是表明，简单使用传输矩阵自然使我们能够获得与上述非单身分式分配量子步行模型相关的拓扑结合状态的显式公式。
It is recently shown by Asahara-Funakawa-Seki-Tanaka that existing index theory for chirally symmetric (discrete-time) quantum walks can be extended to the setting of non-unitary quantum walks. More precisely, they consider a certain non-unitary variant of the two-phase split-step quantum walk as a concrete one-dimensional example, and give a complete classification of the associated index in their study. Note, however, that it remains uncertain whether or not their index gives a lower bound for the number of so-called topologically protected bound states unlike the setting of unitary quantum walks. In fact, the spectrum of a non-unitary operator can be any subset of the complex plane, and so the definition of such bound states is ambiguous in the non-unitary case. The purpose of the present article is to show that the simple use of transfer matrices naturally allows us to obtain an explicit formula for a topologically bound state associated with the non-unitary split-step quantum walk model mentioned above.
