  A measuring apparatus is described by quantum mechanics while it interacts
with the quantum system under observation, and then it must be given a
classical description so that the result of the measurement appears as
objective reality. Alternatively, the apparatus may always be treated by
quantum mechanics, and be measured by a second apparatus which has such a dual
description. This article examines whether these two different descriptions are
mutually consistent. It is shown that if the dynamical variable used in the
first apparatus is represented by an operator of the Weyl-Wigner type (for
example, if it is a linear coordinate), then the conversion from quantum to
classical terminology does not affect the final result. However, if the first
apparatus encodes the measurement in a different type of operator (e.g., the
phase operator), the two methods of calculation may give different results.
