Synthesis of Linear Quantum Systems to Generate a Steady Thermal State
Shan Ma, Matthew J. Woolley, Ian R. Petersen · IEEE Transactions on Automatic Control · 2021
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 stable 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$V=S\operatorname{diag}(\Lambda,\Lambda ) S^{\top }/2$with$\Lambda > I$being a diagonal matrix and$S$being a symplectic matrix will also be considered. Physically, a covariance matrix of the form$V=S\operatorname{diag}(\Lambda,\Lambda ) S^{\top }/2$,$\Lambda > I$, 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.