Experimental investigation of the uncertainty relations with coherent light

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.Comment: 7 pages, 7 figure

Experimental test of the majorization uncertainty relation with mixed states

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.Comment: 19 pages,5 figure

Strong Majorization Uncertainty Relations: Theory and Experiment

In spite of enormous theoretical and experimental progresses in quantum uncertainty relations, the experimental investigation of most current, and universal formalism of uncertainty relations, namely majorization uncertainty relations (MURs), has not been implemented yet. A significant problem is that previous studies on the classification of MURs only focus on their mathematical expressions, while the physical difference between various forms remains unknown. First, we use a guessing game formalism to study the MURs, which helps us disclosing their physical nature, and distinguishing the essential differences of physical features between diverse forms of MURs. Second, we tighter the bounds of MURs in terms of flatness processes, or equivalently, in terms of majorization lattice. Third, to benchmark our theoretical results, we experimentally verify MURs in the photonic systems.Comment: 13 pages, 4 figure