Experimental test of the majorization uncertainty relation with mixed states

TL;DR

This paper experimentally tests the majorization uncertainty relation with mixed quantum states, demonstrating it as the tightest constraint on uncertainty and showing its relation to entropy uncertainty relations.

Contribution

It provides the first experimental verification of majorization uncertainty relations for mixed states, highlighting their optimality over entropy-based relations.

Findings

Majorization uncertainty relation is the tightest constraint for mixed states.

Entropy uncertainty relation derived from majorization is optimal.

Experimental setup effectively prepares and tests mixed quantum states.

Abstract

The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the uncertainty relations which mainly focus on the pure states. In this work we test the novel majorization uncertainty relations of three incompatible observables using a series of mixed states with adjustable mixing degrees, and compare the compactness of various entropy uncertainty relations. The experimental results confirm that for general mixed quantum system, the majorization uncertainty relation tends to be the tightest constraint on uncertainty, and indicate that the entropy uncertainty relation obtained from the majorzation uncertainty relation is the optimal one. Our experimental setup provides an easy means for preparing mixed states, and based on this simple optical elements can be utilized to realize the required quantum states.