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arXiv · 2508.12214

Experimental investigation of uncertainty relations for non-Hermitian operators

Xinzhi Zhao·Xinglei Yu·Wenting Zhou·Chengjie Zhang·Jin-Shi Xu·Chuan-Feng Li·Guang-Can Guo
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Abstract

Uncertainty relations for Hermitian operators have been confirmed through many experiments. However, previous experiments have only tested the special case of non-Hermitian operators, i.e., uncertainty relations for unitary operators. In this study, we explore uncertainty relations for general non-Hermitian operators, which include Hermitian and unitary operators as special cases. We perform experiments with both real and complex non-Hermitian operators for qubit states, and confirm the validity of the uncertainty relations within the experimental error. Our results provide experimental evidence of uncertainty relations for non-Hermitian operators. Furthermore, our methods for realizing and measuring non-Hermitian operators are valuable in characterizing open-system dynamics and enhancing parameter estimation.

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Xinzhi Zhao, Xinglei Yu, Wenting Zhou, Chengjie Zhang, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo. 2025-08-17. Experimental investigation of uncertainty relations for non-Hermitian operators. https://doi.org/10.1103/physrevlett.132.070203

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