  A tight information-theoretic measurement uncertainty relation is
experimentally tested with neutron spin-1/2 qubits. The noise associated to the
measurement of an observable is defined via conditional Shannon entropies and a
tradeoff relation between the noises for two arbitrary spin observables is
demonstrated. The optimal bound of this tradeoff is experimentally obtained for
various non-commuting spin observables. For some of these observables this
lower bound can be reached with projective measurements, but we observe that,
in other cases, the tradeoff is only saturated by general quantum measurements
(i.e., positive-operator valued measures), as predicted theoretically.
