  Traditional uncertainty relations dictate a minimal amount of noise in
incompatible projective quantum measurements. However, not all measurements are
projective. Weak measurements are minimally invasive methods for obtaining
partial state information without projection. Recently, weak measurements were
shown to obey an uncertainty relation cast in terms of entropies. We
experimentally test this entropic uncertainty relation with strong and weak
measurements of a superconducting transmon qubit. A weak measurement, we find,
can reconcile two strong measurements' incompatibility, via backaction on the
state. Mathematically, a weak value -- a preselected and postselected
expectation value -- lowers the uncertainty bound. Hence we provide
experimental support for the physical interpretation of the weak value as a
determinant of a weak measurement's ability to reconcile incompatible
operations.

Quantum Physics