  The impossibility of measuring noncommuting quantum mechanical observables is
one of the most fascinating consequences of the quantum mechanical postulates.
Hence, to date the investigation of quantum measurement and projection is a
fundamentally interesting topic. We propose to test the concept of weak
measurement of noncommuting observables in mesoscopic transport experiments,
using a quasiprobablistic description. We derive an inequality for current
correlators, which is satisfied by every classical probability but violated by
high-frequency fourth-order cumulants in the quantum regime for experimentally
feasible parameters.
