通过连续监测实现投影测量的条件
Conditions for implementing projective measurements through continuous monitoring
中文总结 AI 辅助
本文针对有限维量子系统，明确了连续监测实现投影测量的条件，推导了收敛速率与时间-误差关系，为优化量子测量协议提供了清晰框架。
中文摘要 AI 辅助
投影测量是量子物理学乃至量子信息任务的基础，但其直接实施往往缺乏依据。本文研究体现为量子跳变轨迹的连续监测在何种条件下可随时间实现投影测量。针对有限维量子系统和单一可对角化跳变算子，我们证明检测到的量子跳变统计会强制并允许推断单个量子轨迹在长时间极限下收敛到可观测量的本征态，还确定了与非简并对称 sector 中强对称性存在相关的必要非简并条件。我们推导了收敛速率的解析表达式及有限时间测量中的时间-误差关系。研究结果为理解连续监测中投影测量的出现提供了清晰框架，对实验中量子测量协议的优化具有直接意义。
英文摘要
Projective measurements are foundational for quantum physics in general and quantum information tasks in particular. However, their direct implementation is often not warranted. Here, we investigate under what conditions continuous monitoring that manifests in quantum jump trajectories realises projective measurements over time. Considering finite-dimensional quantum systems and single, diagonalisable jump operators, we show if and how the detected quantum jump statistics force, and allow inferring, the convergence of individual quantum trajectories towards eigenstates of an observable in the long-time limit. We identify a necessary non-degeneracy condition that is related to the presence of a strong symmetry with non-degenerate symmetry sectors. We derive analytical expressions for the rate of convergence and the time-error relationship in finite-time measurements. Our results provide a transparent framework for understanding the emergence of projective measurements from continuous monitoring, with direct implications for the optimisation of quantum measurement protocols in experiments.
