  Unlike regular time evolution governed by the Schr\"odinger equation,
standard quantum measurement appears to violate time-reversal symmetry.
Measurement creates random disturbances (e.g., collapse) that prevents
back-tracing the quantum state of the system. The effect of these disturbances
is explicit in the results of subsequent measurements. In this way, the joint
result of sequences of measurements depends on the order in time in which those
measurements are performed. One might expect that if the disturbance could be
eliminated this time-ordering dependence would vanish. Following a recent
theoretical proposal [A. Bednorz et al 2013 New J. Phys. 15 023043], we
experimentally investigate this dependence for a kind of measurement that
creates an arbitrarily small disturbance, weak measurement. We perform various
sequences of a set of polarization weak measurements on photons. We
experimentally demonstrate that, although the weak measurements are minimally
disturbing, their time-ordering affects the outcome of the measurement sequence
for quantum systems.
