  The Heisenberg-Robertson uncertainty relation quantitatively expresses the
impossibility of jointly sharp preparation of incompatible observables. However
it does not capture the concept of incompatible observables because it can be
trivial even for two incompatible observables. We experimentally demonstrate
the new stronger uncertainty relations proposed by Maccone and Pati [Phys. Rev.
Lett. 113, 260401 (2014)] relating on that sum of variances are valid in a
state-dependent manner and the lower bound is guaranteed to be nontrivial for
two observables being incompatible on the state of the system being measured.
The behaviour we find agrees with the predictions of quantum theory and obeys
the new uncertainty relations even for the special states which trivialize
Heisenberg-Robertson relation. We realize a direct measurement model and give
the first experimental investigation of the strengthened relations.
