线性量子随机系统物理可实现性的一个改进的频域条件
A Modified Frequency Domain Condition for the Physical Realizability of Linear Quantum Stochastic Systems
摘要：
本文讨论线性量子系统频域物理可实现性条件的一个修正形式。考虑开放量子系统，其动力学变量满足开放量子谐振子的正则对易关系，并由线性量子随机微分方程（QSDEs）控制。为了与物理量子系统相对应，这些QSDE必须满足PR条件。我们提供了一个相对简单的证明，PR条件是等效的频域$(J,J)$ -输入输出传递函数的酉性和系统的馈通矩阵的正交性，而无需在以前的工作所需的技术频谱假设。我们还证明了与PR线性量子系统的传递函数相关联的极点和传输零点是彼此关于虚轴的镜像反射。最后给出了一个例子来说明结果。
英文摘要：
This note is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions. We provide a relatively simple proof that the PR condition is equivalent to the frequency domain $(J,J)$-unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.
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