发表机构
Freie Universität Berlin; Helmholtz-Zentrum Berlin für Materialien und Energie（柏林自由大学; 柏林亥姆霍兹材料能源研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出连续量子随机过程的膨胀定理，证明所有连续过程张量可由有界哈密顿量耦合的系统-环境显式描述任意近似，并支撑Choi对偶与连续控制的严格处理。
AI 中文摘要
连接开放量子系统中的数学形式与其底层物理，需要膨胀的概念，即一种将随机动力学与更大空间上的确定性薛定谔演化相桥接的方式。尽管膨胀在文献中对于态、信道和量子梳已是众所周知，但在连续区间上非马尔可夫动力学的完全一般设定中，仍存在实质性空白。在配套工作中，我们引入了连续过程张量（cPT）框架，其中这些过程由多物种玻色子福克空间中$L^2$函数的向量表示。这涵盖了区间上量子系统的所有多时统计。在此，我们提出相应的膨胀定理，并表明所有cPT都可以通过系统与环境由有界哈密顿量耦合的显式闭合描述来任意近似。除了其物理吸引力和证明框架的完备性外，我们表明这种正则表示实际上支撑了该形式，定义了所有cPT的一个易于处理的稠密子空间。这导致了适合连续体的Choi对偶版本，并允许对连续控制进行严格处理。
英文摘要
Connecting mathematical formalism in open quantum systems to its underlying physics necessitates the notion of a dilation, a way to bridge stochastic dynamics with deterministic Schrödinger evolution on a larger space. Although dilations are well known in the literature for states, channels, and quantum combs, there is a substantial gap when it comes to the fully general setting of non-Markovian dynamics on a continuous interval. In an accompanying work, we introduce a continuous process tensor (cPT) framework wherein these processes are represented by vectors in multi-species bosonic Fock spaces of $L^2$ functions. This accommodates all multi-time statistics of a quantum system on an interval. Here, we present a corresponding dilation theorem and show that all cPTs can be approximated arbitrarily well by an explicit closed description with system and environment coupled by a bounded Hamiltonian. As well as its physical appeal and demonstrating completeness of the framework, we show that such regular representations actually underpin the formalism, defining a dense subspace of all cPTs that is easy to handle. This leads to a continuum-suitable version of Choi duality, and permits the rigorous treatment of continuum controls.
Comments7 pages + 28 page SM, 1 figure. Comments welcome!
