  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.

Quantum Physics