论文标题
一类准线性量子随机系统的矩动态和观察者设计
Moment dynamics and observer design for a class of quasilinear quantum stochastic systems
论文作者
论文摘要
本文与一类开放量子系统有关，其动态变量具有代数结构，类似于与有限级系统有关的Pauli矩阵。该系统与外部骨器场相互作用，其Hamiltonian和耦合操作员线性依赖于系统变量。这导致了Hudson-Parthasarathy量子随机微分方程（QSDE），其漂移和分散项是系统变量的仿射和线性函数。 QSDE的准线性导致平均值的易于操作动力学和由真空输入场驱动的系统变量的高阶多点矩。这允许对系统的不变量子状态和一类成本函数的无限渐近生长速率的准截图函数进行封闭式计算。矩动力学的障碍性也用于在基于测量的滤波问题中，用于准式量子植物，这导致了Kalman样量子滤波器。
This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields, and its Hamiltonian and coupling operators depend linearly on the system variables. This results in a Hudson-Parthasarathy quantum stochastic differential equation (QSDE) whose drift and dispersion terms are affine and linear functions of the system variables. The quasilinearity of the QSDE leads to tractable dynamics of mean values and higher-order multi-point moments of the system variables driven by vacuum input fields. This allows for the closed-form computation of the quasi-characteristic function of the invariant quantum state of the system and infinite-horizon asymptotic growth rates for a class of cost functionals. The tractability of the moment dynamics is also used for mean square optimal Luenberger observer design in a measurement-based filtering problem for a quasilinear quantum plant, which leads to a Kalman-like quantum filter.
