[论文解读] New wine in old bottles: Quantum measurement - direct, indirect, weak - with some applications

B. E. Y. Svensson|arXiv (Cornell University)|Feb 23, 2012

Quantum Mechanics and Applications参考文献 33被引用 34

一句话总结

本文使用密度矩阵形式化方法，对量子测量理论进行了自包含且教学性强的综述，重点聚焦于阿哈伦诺夫与瓦伊德曼所发展的弱测量与后选择。通过在弱相互作用至二阶的范围内，从标准量子力学出发推导结果，该文揭示了弱值及相关现象自然涌现，无需引入基础性神秘性；同时推导出开放系统的主方程，并探讨了其在莱格特-加尔格不等式及实验实现中的应用。

ABSTRACT

In this, partly pedagogical review, I attempt to give a self-contained overview of the basis of (non-relativistic) QM measurement theory expressed in density matrix formalism. The focus is on applications to the theory of weak measurement, as developed by Aharonov and Vaidman and their collaborators. Their development of weak measurement combined with what they call 'post-selection' - judiciously choosing not only the initial state of a system ('pre-selection') but also its final state - has received much attention recently. Not the least has it opened up new, fruitful experimental vistas, like novel approaches to amplification. But the approach has also attached to it some air of mystery. I will attempt to 'de-mystify' it by showing that (almost) all results can be derived in a straight-forward way from conventional QM. Among other things, I develop the formalism not only to first order but also to second order in the weak interaction responsible for the measurement. This also allows me to derive, more or less as a by-product, the master equation for the density matrix of an open system in interaction with an environment. One particular application I shall treat of the weak measurement is the so called Leggett-Garg inequalities, a k a 'Bell inequalities in time'. I also give an outline, even if rough, of some of the ingenious experiments that the work by Aharonov, Vaidman and collaborators has inspired. If anything is magic in the weak measurement + post-selection approach, it is the interpretation of the so called weak value of an observable. Is it a bona fide property of the system considered? I have no answer to this question; I shall only exhibit the pros and cons of the proposed interpretation.

研究动机与目标

• 提供使用密度矩阵形式化方法的自包含、教学性强的量子测量理论概述。
• 通过展示弱测量与后选择可从标准量子力学推导，揭示其概念基础，消除其神秘性。
• 将形式化方法从一阶弱相互作用扩展至二阶，以推导开放量子系统的主方程。
• 探讨弱测量在莱格特-加尔格不等式及实验实现中的应用。
• 批判性评估弱值作为系统物理属性的解释。

提出的方法

• 使用密度矩阵表示法构建形式化方法，以描述系统-环境相互作用与测量过程。
• 对弱相互作用进行微扰处理，展开至耦合强度的一阶与二阶。
• 将后选择引入为终态的条件制备，从而定义弱值。
• 作为二阶形式化的副产品，推导出开放系统的主方程。
• 将该框架应用于分析莱格特-加尔格不等式背景下的时间关联。
• 讨论实验意义，特别是放大技术与量子测量协议方面。

实验结果

研究问题

• RQ1 如何在不引入非标准解释的前提下，从标准量子力学推导出弱测量与后选择？
• RQ2 弱相互作用中的二阶项起什么作用？它们如何促成开放系统主方程的推导？
• RQ3 在多大程度上可将弱值解释为量子系统的物理属性？
• RQ4 弱测量与时间关联及莱格特-加尔格不等式有何关联？
• RQ5 该形式化方法对实验量子测量（特别是放大方案）有何启示？

主要发现

• 该形式化方法表明，弱测量与后选择可从标准量子力学中直接推导，消除了大量感知到的神秘性。
• 弱相互作用中的二阶修正项导出了开放量子系统的主方程，证明了该形式化方法的广泛适用性。
• 弱值自然地从密度矩阵形式化中涌现，并非本质上非物理，尽管其解释仍存在争议。
• 该方法为分析时间关联提供了连贯的框架，与莱格特-加尔格不等式的检验密切相关。
• 本文概述了该理论如何启发创新实验，特别是在量子放大与弱值探测方面。
• 分析表明，弱测量的“神奇”之处并非源于基础性新意，而在于条件测量与微扰展开的数学结构。