  Postselected quantum metrological scheme is especially advantageous when the
final measurements are either very noisy or expensive in practical experiments.
In this work, we put forward a general theory on the compression channels in
postselected quantum metrology. We define the basic notions characterizing the
compression quality and illuminate the underlying structure of lossless
compression channels. Previous experiments on Postselected optical phase
estimation and weak-value amplification are shown to be particular cases of
this general theory. Furthermore, for two categories of bipartite systems, we
show that the compression loss can be made arbitrarily small even when the
compression channel acts only on one subsystem. These findings can be employed
to distribute quantum measurements so that the measurement noise and cost are
dramatically reduced.
