Synthesis of Linear Quantum Systems to Generate a Steady Thermal State

• 成果类型: Article
• 署名作者: Ma, Shan; Woolley, Matthew James; Petersen, Ian R.
• 署名单位: Central South University; Peng Cheng Laboratory; University of New South Wales Sydney; Australian Defense Force Academy; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3079291
• 发表日期: 2022
• 页码: 2131-2137
• 关键词: Covariance assignment; covariance matrix; linear quantum system; system synthesis

摘要

The purpose of this article is to synthesize a linear quantum system, which is strictly stable and has a steady thermal state. Specifically, we give a parameterization of a class of sta- ble linear quantum systems that have V = tau I/2, tau > 1, as their steady covariance matrsices. This is physically important since the covariance matrix tau I/2, tau > 1, corresponds to a quantum thermal state. Hence, we can say that these systems will asymptotically evolve into a quantum thermal state. An extension to the case where V = S diag (Lambda, Lambda)S-T/2 with Lambda > I being a diagonal matrix and S being a symplectic matrix will also be considered. Physically, a covariance matrix of the form V = S diag (Lambda, Lambda)S-T/2, Lambda > I, corresponds to a mixed Gaussian quantum state. So, we can alternatively say that the corresponding linear quantum systems will asymptotically evolve into a mixed Gaussian quantum state.