论文标题
部分可观测时空混沌系统的无模型预测
Spectral mapping theorem of an abstract non-unitary quantum walk
论文作者
论文摘要
本文延续了本文的两位作者的先前作品（量子信息过程（2019）），介绍了手学对称统一操作员的光谱映射属性。在物理学中，他们将非自动的时间进化操作员考虑在开放系统中考虑量子行走。在本文中，我们将上述结果推广到包括手性对称的非独立操作员，其硬币操作员只有两个特征值。结果，此类非独立运算符的光谱被包括在（可能是非单位）圆和复杂平面中的真实轴中。我们还举例说明了我们的抽象结果，例如Mochizuki等人定义的非单身量子步行。此外，我们向Ihara Zeta函数提出了应用程序，并在常规图上进行了与量子步道相关的随机步行。
This paper continues the previous work (Quantum Inf. Process (2019)) by two authors of the present paper about a spectral mapping property of chiral symmetric unitary operators. In physics, they treat non-unitary time-evolution operators to consider quantum walks in open systems. In this paper, we generalize the above result to include a chiral symmetric non-unitary operator whose coin operator only has two eigenvalues. As a result, the spectra of such non-unitary operators are included in the (possibly non-unit) circle and the real axis in the complex plane. We also give some examples of our abstract results, such as non-unitary quantum walks defined by Mochizuki et al. Moreover, we present an application to the Ihara zeta functions and correlated random walks on regular graphs, which are not quantum walks.
