标题： 条件输出，决策时间的分布和基于测量的反馈方案用于简单量子系统的连续弱线性测量 显示英文标题

标题： Conditioned outputs, distribution of decision times and measurement-based feedback scheme for continuous weak linear measurement of a simple quantum system

摘要： 我们研究了连续弱线性测量（CWLM）过程中量子测量过程的特殊性。 作为工具，我们采用了一种高效的数值模拟方案，该方案允许我们生成被测系统状态的单个量子轨迹以及记录的探测器信号，并研究这些轨迹在有和没有后选择条件下的统计特性。 在这个方案中，用一个与被测量子系统弱耦合的量子比特来建模线性探测器，并在每次模拟步骤的时间间隔后接受投影测量和重新初始化。 我们解释了在这种情况下该方案能够准确描述CWLM的条件。 我们将研究限制在量子比特非破坏性测量上。 量子比特最初处于两个量子态的等权重叠加态。 随着时间推移，探测器信号积累并且叠加态被破坏。 分辨量子态所需时间和破坏叠加态所需时间在同一数量级。 我们通过数值证明了一个相当反直觉的事实：最终态条件下的平均探测器输出不依赖于时间。 看起来从一开始，量子比特就知道它处于哪个状态。 我们研究了决策时间的统计特性，其中决策时间定义为沿特定轨迹的密度矩阵达到接近其中一个最终状态的阈值所需的时长。 这种统计特性有助于估算决定性的CWLM可以多快实现。 基于此，我们设计并研究了一个简单的反馈方案，试图让量子比特保持在等权重叠加态。 使用探测器读数来判断量子比特处于哪个状态以及应施加哪种校正旋转以将其带回叠加态。 我们展示了如何优化反馈参数并迈向更高效的反馈方案。 显示英文摘要

摘要： We address the peculiarities of the quantum measurement process in the course of a continuous weak linear measurement (CWLM). As a tool, we implement an efficient numerical simulation scheme that allows us to generate single quantum trajectories of the measured system state as well as the recorded detector signal, and study statistics of these trajectories with and without post-selection. In this scheme, a linear detector is modelled with a qubit that is weakly coupled to the quantum system measured and is subject to projective measurement and re-initialization after a time interval at each simulation step. We explain the conditions under which the scheme provides an accurate description of CWLM. We restrict ourselves to a qubit non-demolition measurement. The qubit is initially in an equal-weight superposition of two quantum states. In the course of time, the detector signal is accumulated and the superposition is destroyed. The times required to resolve the quantum states and to destroy the superposition are of the same order. We prove numerically a rather counter intuitive fact: the average detector output conditioned on the final state does not depend on time. It looks like from the very beginning, the qubit knows in which state it is. We study statistics of decision times where the decision time is defined as time required for the density matrix along a certain trajectory to reach a threshold where it is close to one of the resulting states. This statistics is useful to estimate how fast a decisive CWLM can be. Basing on this, we devise and study a simple feedback scheme that attempts to keep the qubit in the equal-weight superposition. The detector readings are used to decide in which state the qubit is and which correction rotation to apply to bring it back to the superposition. We show how to optimize the feedback parameters and move towards more efficient feedback schemes.