# Experimental investigation of the uncertainty relations with coherent light

## TL;DR

This paper experimentally investigates variance-based and majorization uncertainty relations in a two-dimensional quantum system using coherent light, demonstrating the ensemble nature of quantum uncertainty through polarization measurements.

## Contribution

It provides the first experimental verification of the optimal direct-sum majorization uncertainty relation using polarization density matrices.

## Key findings

- Lorenz curves accurately verify majorization uncertainty relations
- Uncertainty relations are confirmed as ensemble properties of quantum systems
- Experimental results support the theoretical optimality of the majorization relation

## Abstract

Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system.Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system.