  Measurements map the value of a target observable onto a meter shift,
resulting in a meter readout that combines the initial statistics of the meter
state with the quantum statistics of the target observable. Even in the limit
of weak measurement interactions, some information about the fluctuations of
the target observable can be extracted from the change in the readout
fluctuations caused by the measurement interaction. Here, we apply the
Heisenberg picture to analyze the changes in the meter readout statistics
caused by sufficiently weak measurement interactions, including the effects of
non-linearities in the meter response. When additional information is obtained
in a subsequent measurement of the system, the meter fluctuations are modified
based on the post-selected statistics of the target observable. In addition,
our analysis reveals a direct modification of the meter fluctuations due to the
dependence of the post-selection probability on the dynamics induced by the
meter in the measurement interaction. We point out that the quantum formalism
makes it difficult to distinguish this dynamic term from the physical
fluctuations of the target observable and stress the importance of
distinguishing between genuine conditional fluctuations of the target
observable and the dynamic pseudovariance associated with the measurement
back-action.
