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The uncertainty relation lies at the heart of quantum theory and behaves as anon-classical constraint on the indeterminacies of incompatible observables ina system. In the literature, many experiments have been devoted to the test ofthe uncertainty relations which mainly focus on the pure states. In this workwe test the novel majorization uncertainty relations of three incompatibleobservables using a series of mixed states with adjustable mixing degrees, andcompare the compactness of various entropy uncertainty relations. Theexperimental results confirm that for general mixed quantum system, themajorization uncertainty relation tends to be the tightest constraint onuncertainty, and indicate that the entropy uncertainty relation obtained fromthe majorzation uncertainty relation is the optimal one. Our experimental setupprovides an easy means for preparing mixed states, and based on this simpleoptical elements can be utilized to realize the required quantum states.

Experimental test of the majorization uncertainty relation with mixed states