Experimental investigation of majorization uncertainty relations in the high-dimensional systems

TL;DR

This paper experimentally investigates majorization uncertainty relations in high-dimensional quantum systems, comparing different formulations and demonstrating their strengths and distinctions through empirical data.

Contribution

First experimental study of majorization uncertainty relations in high-dimensional systems, analyzing direct-product and direct-sum formulations and their comparative advantages.

Findings

Different Schur-concave functions reveal unique advantages of MUR types.

Three-measurement MUR can be significantly stronger than pairwise relations.

Experimental verification advances understanding of quantum uncertainty principles.

Abstract

Uncertainty relation is not only of fundamental importance to quantum mechanics, but also crucial to the quantum information technology. Recently, majorization formulation of uncertainty relations (MURs) have been widely studied, ranging from two measurements to multiple measurements. Here, for the first time, we experimentally investigate MURs for two measurements and multiple measurements in the high-dimensional systems, and study the intrinsic distinction between direct-product MURs and direct-sum MURs. The experimental results reveal that by taking different nonnegative Schur-concave functions as uncertainty measure, the two types of MURs have their own particular advantages, and also verify that there exists certain case where three-measurement majorization uncertainty relation is much stronger than the one obtained by summing pairwise two-measurement uncertainty relations. Our work not only fills the gap of experimental studies of majorization uncertainty relations, but also represents an advance in quantitatively understanding and experimental verification of majorization uncertainty relations which are universal and capture the essence of uncertainty in quantum theory.