对易关系的直接实验检验*

doi:10.7523/j.ucas.2023.052

中国科学院大学学报

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对易关系的直接实验检验^*

王慧, 王双, 乔从丰^†

中国科学院大学物理科学学院北京 100049

收稿日期:2023-04-06 修回日期:2023-05-10 发布日期:2023-05-10
通讯作者: †E-mail, qiaocf@ucas.ac.cn
基金资助:
^*国家自然科学基金（11975236,12235008）和中国科学院大学自主安排项目资助

Direct experimental investigation of commutation relation

WANG Hui, WANG Shuang, QIAO Congfeng^†

School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2023-04-06 Revised:2023-05-10 Published:2023-05-10

摘要/Abstract

摘要： 正则对易关系是量子理论的标志之一。实验检验对易关系的一种方法是根据其定义展开序列测量,但这种方法对不相容观测量之间的内在关联验证是有限的。在本文中,我们基于弱测量的双态矢量形式,将观测量的本征态作为前选择态,构造出另一个不相容观测量的弱值。弱值建立了两个非对易观测量之间的联系,而且和后选择概率共同决定了对易关系的期望值。实验使用高稳定性的相干光在复合路径干涉中实现弱值的提取。实验结果与理论一致,完成了对泡利算符对易关系的直接检验,为进一步理解对易关系和量子不确定关系提供了新的实验依据。

关键词: 对易关系, 弱值, 弱测量, 相干光

Abstract: The canonical commutation relation is one of the hallmarks of quantum theory. One method of testing commutation relation is to perform sequential measurements according to it's definition, but the verification of intrinsic association between incompatible observables has been rather limited. In this study, we construct the weak value of another incompatible observable based on the two-state vector formalism of weak measurement, where the eigenstate of one observable act as pre-selective state. The weak value establishes a correlation between two noncommuting observables, and determines the expectation value of commutation relation together with the post-selection probability. The experiments realize the extraction of weak values using composite path interference with high-stability coherent light. Experimental results agree with the theory and accomplish a direct test of commutation relation for Pauli operators, which provides a new experimental basis for further understanding of the commutation relation and quantum uncertainty relations.

Key words: commutation relation, weak value, weak measurement, coherent light

中图分类号:

O413

王慧, 王双, 乔从丰. 对易关系的直接实验检验^*[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2023.052.

WANG Hui, WANG Shuang, QIAO Congfeng. Direct experimental investigation of commutation relation[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2023.052.

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对易关系的直接实验检验^*

Direct experimental investigation of commutation relation

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