Experimental investigation of the uncertainty relations with coherent light

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.

Experimental test of the majorization uncertainty relation with mixed states

“…The investigation of the direct sum majorization uncertainty relation using the coherent lights was carried out in Ref. [23] by measuring the Lorenz curves. For mixed system, a test of the variance-based and the related entropic uncertainty relations of two qubit observables were carried out using the neutron spins [24].…”