  The action of qubit channels on projective measurements on a qubit state is
used to establish an equivalence between channels and properties of generalized
measurements characterized by bias and sharpness parameters. This can be
interpreted as shifting the description of measurement dynamics from the
Schrodinger to the Heisenberg picture. In particular, unital (non-unital)
quantum channels are shown to induce unbiased (biased) measurements. The
Markovian channels are found to be equivalent to measurements for which
sharpness is a monotonically decreasing function of time. These results are
illustrated by considering various noise channels. Further, the effect of bias
and sharpness parameters on the energy cost of a measurement and its interplay
with the non-Markovian dynamics is also discussed.
