  Weak values arise experimentally as conditioned averages of weak (noisy)
observable measurements that minimally disturb an initial quantum state, and
also as dynamical variables for reduced quantum state evolution even in the
absence of measurement. These averages can exceed the eigenvalue range of the
observable ostensibly being estimated, which has prompted considerable debate
regarding their interpretation. Classical conditioned averages of noisy signals
only show such anomalies if the quantity being measured is also disturbed prior
to conditioning. This fact has recently been rediscovered, along with the
question whether anomalous weak values are merely classical disturbance
effects. Here we carefully review the role of the weak value as both a
conditioned observable estimation and a dynamical variable, and clarify why
classical disturbance models will be insufficient to explain the weak value
unless they can also simulate other quantum interference phenomena.
