非爆破量子轨道的大时间行为和收敛速度
Large Time Behaviour and Convergence Rate for Non Demolition Quantum Trajectories
摘要：
一个连续时间测量的量子系统S通常由一个跳扩散随机微分方程描述。这样的方程称为随机主方程，其解称为量子轨迹。这个解实际上描述了S态的演化。在量子非破坏测量的背景下，我们研究了该解的大时间行为。它严格表明，对于大的时间，这个解决方案的行为，如果一个直接冯诺依曼测量已在时间0。特别地，该解收敛到与波包约化公设有关的随机纯态。利用Girsanov变换的理论，我们精确地确定了这个随机状态的指数收敛速度。本文还研究了状态估计（用于实验）的重要问题。
英文摘要：
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory. This solution describes actually the evolution of the state of S. In the context of Quantum Non Demolition measurement, we investigate the large time behavior of this solution. It is rigorously shown that, for large time, this solution behaves as if a direct Von Neumann measurement has been performed at time 0. In particular the solution converges to a random pure state which is related to the wave packet reduction postulate. Using theory of Girsanov transformation, we determine precisely the exponential rate of convergence towards this random state. The important problem of state estimation (used in experiment) is also investigated.
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。
