  This thesis is concerned with retrodiction and measurement in quantum optics.
The latter of these two concepts is studied in particular form with a general
optical multiport device, consisting of an arbitrary array of beam-splitters
and phase-shifters. I show how such an apparatus generalizes the original
projection synthesis technique, introduced as an in principle technique to
measure the canonical phase distribution. Just as for the original projection
synthesis, it is found that such a generalised device can synthesize any
general projection onto a state in a finite dimensional Hilbert space. One of
the important findings of this thesis is that, unlike the original projection
synthesis technique, the general apparatus described here only requires a
classical, that is a coherent, reference field at the input of the device. Such
an apparatus lends itself much more readily to practical implementation and
would find applications in measurement and predictive state engineering.
  If we relax the above condition to allow for just a single non-classical
reference field, we show that the apparatus is capable of producing a
single-shot measure of canonical phase. That is, the apparatus can project onto
any one of an arbitrarily large subset of phase eigenstates, with a probability
proportional to the overlap of the phase state and the input field. Unlike the
original projection synthesis proposal, this proposal requires a binomial
reference state as opposed to a reciprocal binomial state. We find that such a
reference state can be obtained, to an excellent approximation, from a suitably
squeezed state.
  The analysis of these measurement apparatuses is performed in the less usual,
but completely rigorous, retrodictive formalism of quantum mechanics.

Quantum Physics