  Uncertainty relation is not only of fundamental importance to quantum
mechanics, but also crucial to the quantum information technology. Recently,
majorization formulation of uncertainty relations (MURs) have been widely
studied, ranging from two measurements to multiple measurements. Here, for the
first time, we experimentally investigate MURs for two measurements and
multiple measurements in the high-dimensional systems, and study the intrinsic
distinction between direct-product MURs and direct-sum MURs. The experimental
results reveal that by taking different nonnegative Schur-concave functions as
uncertainty measure, the two types of MURs have their own particular
advantages, and also verify that there exists certain case where
three-measurement majorization uncertainty relation is much stronger than the
one obtained by summing pairwise two-measurement uncertainty relations. Our
work not only fills the gap of experimental studies of majorization uncertainty
relations, but also represents an advance in quantitatively understanding and
experimental verification of majorization uncertainty relations which are
universal and capture the essence of uncertainty in quantum theory.
