Experimental investigation of uncertainty relations for non-Hermitian operators

TL;DR

This paper experimentally investigates uncertainty relations for general non-Hermitian operators, extending previous work beyond Hermitian and unitary cases, and demonstrates their validity for qubit states.

Contribution

It provides the first experimental validation of uncertainty relations for general non-Hermitian operators, including methods for their realization and measurement.

Findings

Uncertainty relations hold for non-Hermitian operators within experimental error.

Experimental methods for realizing and measuring non-Hermitian operators are developed.

Results are applicable to open-system dynamics and parameter estimation.

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.