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arXiv 2610.13622quant-ph
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奇异量子通道的操作特征

Operational signatures of exceptional quantum channels

Instituto de Física, Universidade Federal de Alagoas（阿拉戈斯联邦大学物理研究所）

Paulo A. Brandão

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AI总结：

该研究构建了不依赖哈密顿量或主方程的奇异点操作理论，通过完全正保迹量子通道的若尔当链定义奇异通道，将奇异点物理特性与实验可测量量关联。

摘要：

奇异点（EPs）通常被定义为非厄米哈密顿量的缺陷简并，在完全开放量子动力学中则为刘维尔生成元的缺陷简并。本文构建了一种不依赖哈密顿量或主方程的奇异点操作理论，基础动力学对象是完全正保迹（CPTP）量子通道Φ，将其应用整数次n，物理数据为与态ρ和可观测量A相关的概率p_n^A(x|ρ)，其中x为测量结果。我们通过Φ的非平凡若尔当链定义奇异通道，证明m阶若尔当块会生成最大次数为m-1的离散多项式指数项，这将奇异点的物理特性与实验中可直接测量的量联系起来。

英文摘要：

Exceptional points (EPs) are usually introduced as defective degeneracies of non-Hermitian Hamiltonians and, in fully open quantum dynamics, of Liouvillian generators. Here we formulate an operational theory of exceptional points that does not invoke a Hamiltonian or a master equation. The primitive dynamical object is a completely positive trace-preserving (CPTP) quantum channel $Φ$, applied an integer number $n$ of times, while physical data are probabilities $p_n^{\mathbf A}(x|ρ)$ associated with states $ρ$ and observables $\mathbf A$ having measurements results $x$. We define exceptional channels through nontrivial Jordan chains of $Φ$ and show that a Jordan block of order $m$ generates discrete polynomial-exponential terms with maximal degree $m-1$. This places the physics of exceptional points in contact with what can be directly measured in experiments.

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