发表机构
Ben-Gurion University of the Negev; University of Florida; Department of Mathematical Sciences and QMATH, University of Copenhagen（内盖夫本-古里安大学; 佛罗里达大学; 哥本哈根大学数学科学系与QMATH中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无序环境中的离散时间量子轨迹，在淬火Doeblin条件下建立了随机后验律等变族的唯一存在性，并证明遍历环境下时间平均的收敛性、方差渐近性、中心极限定理及Berry-Esseen界。
AI 中文摘要
我们研究有限维系统在无序环境中的离散时间量子轨迹，其中每一步应用的仪器由一个可逆的保测动力系统决定。对于标准Borel结果空间上的一般量子仪器，我们为固定无序实现和给定初始状态构造了测量结果序列的淬火概率律。在具有均匀确定性次极小化常数和环境依赖次极小化概率测度的淬火Doeblin条件下，我们建立了随机后验律的等变族的唯一存在性，并将其重心确定为相关非选择性信道余循环的唯一动态平稳态。若环境是遍历的，我们证明了一个对每个可测初始状态选择都成立的逐点遍历定理：对于几乎每个无序实现，在相应淬火律下，后验状态的时间平均值几乎必然收敛到唯一动态平稳态的无序平均。对于遍历环境，我们建立了淬火方差渐近性，并且当渐近方差为正时，建立了中心极限定理和由环境与后验状态的有界可测实值函数生成的加性泛函的标准化Berry-Esseen界。这些结果对每个可测初始状态和几乎每个无序实现都成立。然后我们证明，仪器和后验状态的平稳退火联合过程继承了仪器过程的α混合性，直到一个指数衰减项。最后，我们提供了涉及完美和不完美测量的例子类别，包括具有连续或有限结果空间的模型，这些模型满足所考虑的Doeblin条件。
英文摘要
We study discrete-time quantum trajectories of a finite-dimensional system in a disordered environment, where the instrument applied at each step is determined by an invertible measure-preserving dynamical system. For general quantum instruments on a standard Borel outcome space, we construct the quenched probability law on sequences of measurement outcomes for a fixed realization of the disorder and a given initial state. Under a quenched Doeblin condition with a uniform deterministic minorization constant and an environment-dependent minorizing probability measure, we establish the existence and uniqueness of an equivariant family of random posterior laws and identify its barycenter as the unique dynamically stationary state for the associated non-selective channel cocycle. If the environment is ergodic, we prove a pathwise ergodic theorem valid for every measurable choice of initial state: for almost every realization of the disorder, time averages of posterior states converge almost surely under the corresponding quenched law to the disorder average of the unique dynamically stationary state. For an ergodic environment, we establish quenched variance asymptotics and, when the asymptotic variance is positive, a central limit theorem and standardized Berry--Esseen bounds for additive functionals generated by bounded measurable real-valued functions of the environment and posterior state. These results hold for every measurable initial state and almost every disorder realization. We then show that the stationary annealed joint process of instruments and posterior states inherits the $α$-mixing of the instrument process, up to an exponentially decaying term. Finally, we provide classes of examples involving perfect and imperfect measurements, including models with continuous or finite outcome spaces, that satisfy the standing Doeblin condition.
Comments71 pages, 3 tables, no figures
