  A novel method was recently proposed and experimentally realized for
characterizing a quantum state by directly measuring its complex probability
amplitudes in a particular basis using so-called weak values. Recently Vallone
and Dequal showed theoretically that weak measurements are not a necessary
condition to determine the weak value [Phys. Rev. Lett. 116, 040502 (2016)].
Here we report a measurement scheme used in a matter-wave interferometric
experiment in which the neutron path system's quantum state was characterized
via direct measurements using both strong and weak interactions. Experimental
evidence is given that strong interactions outperform weak ones. Our results
are not limited to neutron interferometry, but can be used in a wide range of
quantum systems.
