arXiv 2205.040802022-05-25quant-phcs.SYeess.SYmath.OC

线性量子系统教程

Linear quantum systems: a tutorial

Guofeng Zhang, Zhiyuan Dong

备注：: 55 pages, 4 figures, to appear in Annual Reviews in Control

摘要：

本教程的目的是简要介绍线性量子控制系统。首先给出了线性量子控制系统的数学模型，然后给出了与量子信息科学中的几个重要概念如无消相干子系统、量子非破坏变量和反作用规避测量密切相关的一些基本控制理论概念如稳定性、可控性和可观性.在此基础上，引入了量子高斯态，特别是提出了一种信息论测不准关系，它比著名的Heisenberg测不准关系对混合高斯态给出了更好的上界。量子卡尔曼滤波器是针对量子线性系统提出的，它是经典（即非量子力学）线性系统卡尔曼滤波器的量子类比。记录了量子线性系统的量子Kalman正则分解，并通过最近的一个实验说明了它的应用。由于单光子和多光子态是量子信息技术中非常有用的资源，本文研究了量子线性系统对这两种输入的响应。最后，简单介绍了量子线性系统的相干反馈控制，并用最近的一个实验来证明量子线性系统和网络理论的有效性。简单介绍了量子线性系统的dback控制，并用最近的一个实验来证明量子线性系统和网络理论的有效性。

英文摘要：

The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum non-demolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is presented which often gives a better bound for mixed Gaussian states than the well-known Heisenberg uncertainty relation. The quantum Kalman filter is presented for quantum linear systems, which is the quantum analogy of the Kalman filter for classical (namely, non-quantum-mechanical) linear systems. The quantum Kalman canonical decomposition for quantum linear systems is recorded, and its application is illustrated by means of a recent experiment. As single- and multi-photon states are useful resources in quantum information technology, the response of quantum linear systems to these types of input is presented. Finally, coherent feedback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.dback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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