Networks of open quantum systems with feedback have become an active area of research for applications such as quantum control, quantum communication and coherent information processing. A canonical formalism for the interconnection of open quantum systems using quantum stochastic differential equations (QSDEs) has been developed by Gough, James and co-workers and has been used to develop practical modeling approaches for complex quantum optical, microwave and optomechanical circuits/networks. In this paper we fill a significant gap in existing methodology by showing how trapped modes resulting from feedback via coupled channels with finite propagation delays can be identified systematically in a given passive linear network. Our method is based on the Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued functions, which has been applied in the past to analog electronic networks. Our results provide a basis for extending the Quantum Hardware Description Language (QHDL) framework for automated quantum network model construction (Tezak et al. in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, 2012) to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay.

中文翻译：

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时滞线性量子随机网络中的陷阱模式

具有反馈的开放式量子系统网络已成为诸如量子控制，量子通信和相干信息处理等应用研究的活跃领域。Gough，James和他的同事已经开发出一种使用量子随机微分方程（QSDE）互连开放量子系统的规范形式，并已被用于开发用于复杂量子光学，微波和光机械电路/网络的实用建模方法。在本文中，我们通过展示如何在给定的无源线性网络中系统地识别出具有有限传播延迟的耦合通道的反馈所导致的陷波模式，从而填补了现有方法的重大空白。我们的方法基于内部矩阵值函数的Blaschke-Potapov乘法分解定理，过去已应用于模拟电子网络。我们的结果为扩展用于自动量子网络模型构建的量子硬件描述语言（QHDL）框架提供了基础（Tezak等人，在Philos。Trans。R. Soc。A，数学物理工程科学370（1979）中：5270-5290，2012），以有效地处理各个组件互连具有相关信号传播时间延迟的场景。