This paper provides a stabilizing method for preparation of quantum Gaussian states by utilizing continuous measurement. We first present a necessary and sufficient condition for the Riccati equation of the covariance matrix of the Gaussian states to have a unique stabilizing steady solution. Then general parametric conditions of how to prepare a Gaussian state with desired covariance matrix are provided. These conditions are much weaker than those required when preparing Gaussian states via dissipation-induced approach. Thus, our method provides more degrees of freedom to choose the system Hamiltonian and the system–environment coupling operators. These results may benefit practical experimental implementations in preparing quantum Gaussian states.

Publication:

Automatica, Volume 164, June 2024, 111622

http://dx.doi.org/10.1016/j.automatica.2024.111622

Author:

Liying Bao

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

University of Chinese Academy of Sciences, Beijing 100049, China

Civil Aviation University of China, Tianjin 300300, China

Bo Qi

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

University of Chinese Academy of Sciences, Beijing 100049, China

Email: qibo@amss.ac.cn

Daoyi Dong

School of Engineering, Australian National University, Canberra, ACT 2601 Australia