标题： 确定流形上的约束和连续测量量子系统的低维解公式 显示英文标题

标题： Confinement to deterministic manifolds and low-dimensional solution formulas for continuously measured quantum systems

摘要： 量子系统在连续弱测量下遵循随机微分方程（SDE）。 根据实际的随机测量结果，量子态可以逐步扩散，先验地在状态空间的所有方向上扩散。 本说明指出，在一些对量子工程感兴趣的设置中，这种扩散实际上发生在低维空间中。 即，状态保持在一个低维非线性流形内，通常是时变的，但与测量结果无关。 本说明提供了在几种此类设置中计算随机演化状态的相应低维表达式：任意维度的量子非破坏性测量；谐振子的正交测量（线性量子系统）；以及多粒子量子系统中的子系统测量。 提出了一种代数准则，可以直接检查在额外动力学下这些低维流形是否存在或是否持续存在。 显示英文摘要

摘要： Quantum systems under continuous weak measurement follow stochastic differential equations (SDE). Depending on the stochastic measurement results indeed, the quantum state can progressively diffuse, a priori in all directions of state space. This note draws attention to the observation that, in several settings of interest for quantum engineering, this diffusion in fact takes place in low dimension. Namely, the state remains confined in a low-dimensional nonlinear manifold, often time-dependent, but independent of the measurement results. The note provides the corresponding low-dimensional expressions for computing the stochastically evolving state in several such settings: quantum non-demolition measurement in arbitrary dimensions; quadrature measurements on a harmonic oscillator (linear quantum system); and subsystem measurement in multi-partite quantum systems. An algebraic criterion is proposed to directly check when such low-dimensional manifolds exist or survive under additional dynamics.