[论文解读] Quantum- vs. Macro- Realism: What does the Leggett-Garg Inequality actually test?

O. J. E. Maroney, Christopher G. Timpson|arXiv (Cornell University)|Dec 18, 2014

Quantum Mechanics and Applications参考文献 36被引用 24

一句话总结

本文澄清了，Leggett-Garg 不等式本身并不直接检验宏观实在论，而是检验测量中的操作性无扰动。它表明，违反该不等式仅能排除一种特定的、较弱形式的宏观实在论——即操作性本征态混合实在论——同时区分了操作性非侵入性与本体论非侵入性，揭示出仅凭该不等式本身无法证伪宏观实在论。

ABSTRACT

Macroscopic Realism (MR) says that a macroscopic system is always determinately in one or other of the macroscopically distinguishable states available to it. The Leggett-Garg (LG) inequality was derived to allow experimental test of whether or not this doctrine is true; it is also often thought of as a temporal version of a Bell-inequality. Despite recent interest in the inequality, controversy remains regarding what would be shown by its violation. Here we resolve this controversy, which arises due to an insufficiently general and model-independent approach to the question so far. We argue that LG's initial characterisation of MR does not pick out a particularly natural realist position, so we articulate an operationally well-defined and well-motivated position in its place. We show that much weaker conditions than LG's are sufficient to derive the inequality: in the first instance, its violation only demonstrates that certain measurements fail to be non-disturbing at the operational level. We articulate three distinct species of MR-ist position, and argue that it is only the first of these which can be refuted by LG inequality violation. This first position is an attractive one, so ruling it out remains of interest, however. A crucial role is played in LG's argument by the assumption of noninvasive measurability. We show that this notion is ambiguous between the weaker notion of disturbance at the operational level, and the stronger notion of invasiveness at the ontic level of properties of the system. Ontic noninvasiveness would be required to rule out MR per se but this property is not entailed by MR, and its presence cannot be established in a model-independent way. It follows that despite the formal parallels, Bell's and LG's inequalities are not methodologically on a par. We close with some reflections on the implications of our analysis for the pedagogy of quantum superposition.

研究动机与目标

• 解决关于 Leggett-Garg 不等式在宏观实在论关系中实际检验内容的持续争议。
• 澄清操作性非扰动与本体论非侵入性之间的区别，表明二者并不等价。
• 识别并形式化三种不同的宏观实在论立场，区分哪些可被不等式违反所排除。
• 论证只有其中一种——操作性本征态混合宏观实在论——会被 Leggett-Garg 不等式的违反所证伪。
• 纠正一种误解，即宏观实在论整体被实验上违反该不等式所排除。

提出的方法

• 使用本体模型框架，从操作性和本体两个层面正式分析测量扰动。
• 在最小假设下推导 Leggett-Garg 不等式，表明其仅由操作性非扰动即可导出。
• 引入并定义三种不同的宏观实在论立场：操作性本征态混合实在论、操作性本征态支持实在论以及超本征态支持实在论。
• 分析非侵入可测量性的角色，将其与操作性非扰动区分开来，并表明其并非由宏观实在论所蕴含。
• 将不等式应用于具有联合概率和相关函数的三时刻测量情景，以简化形式推导出不等式。
• 证明违反要求在边缘统计中存在可检测的扰动，即非零的 D 项，意味着存在操作性扰动。

实验结果

研究问题

• RQ1 Leggett-Garg 不等式违反在宏观实在论立场中具体排除了什么？
• RQ2 操作性非扰动与本体论非侵入性有何不同，为何这一区别至关重要？
• RQ3 宏观实在论整体能否被 Leggett-Garg 不等式证伪，还是仅能证伪其受限版本？
• RQ4 非侵入可测量性假设是否足以排除宏观实在论，且该假设是否由宏观实在论所蕴含？
• RQ5 在量子预测的背景下，Leggett-Garg 不等式的正确操作性解释是什么？

主要发现

• Leggett-Garg 不等式的违反仅排除操作性本征态混合宏观实在论，而非宏观实在论整体。
• 该不等式仅由较弱的条件——操作性非扰动——导出，而非本体论非侵入性。
• 本体论非侵入性（用于排除宏观实在论所必需）并不被宏观实在论所蕴含，也无法在无模型依赖的方式下确立。
• 不等式推导中非零 D 项的存在表明存在可检测的操作性扰动，这是违反的必要条件但非充分条件。
• 不等式的简化形式 ⟨Q⁺⟩_LG = 2D₂₊₁₊₁ + 4P(Q₁=+1,Q₂=+1,Q₃=+1) − 1 表明，违反要求测量 M₂ 对 M₃ 统计产生扰动。
• 双缝实验被用作尾声，以说明宏观实在论并不蕴含非侵入性，从而强化了操作性与本体论层面之间的区别。