  Quantum measurements generally introduce perturbations into the subsequent
evolution of the measured system. Furthermore, a projective measurement cannot
decrease the uncertainty on the system if the outcome is ignored; that is, the
von Neumann entropy cannot decrease. However, under certain sound assumptions
and using the quantum violation of Leggett-Garg inequalities, we demonstrate
that this property is not inherited by a faithful classical causal simulation
of a measurement process. In the simulation, a measurement erases previous
information by performing a partial reset on the system. Thus, the measuring
device acts as a low-temperature bath absorbing entropy from the measured
system. Information erasure is a form of Spekkens' preparation contextuality.
Our proof is straightforward if one assumes that maximal ignorance of the
quantum state is compatible with maximal ignorance of the classical state. We
also employ a weaker hypothesis. Information erasure is related to a theorem of
Leifer and Pusey, which states that time symmetry implies retrocausality. In
light of our findings, we discuss Spekkens' preparation contextuality, as well
as a weakness in the hypothesis of time symmetry as defined by Leifer and
Pusey.
