  The problem of the estimation of multiple phases (or of commuting unitaries)
is considered. This is a sub-model of the estimation of a completely unknown
unitary operation where it has been shown in recent works that there are
considerable improvements by using entangled input states and entangled
measurements. Here it is shown that when estimating commuting unitaries, there
is practically no advantage in using entangled input states or entangled
measurements.
