Direct experimental investigation of commutation relation

doi:10.7523/j.ucas.2023.052

Abstract

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

CLC Number:

O413

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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