  We investigate the simultaneous estimation of $n$ not necessarily identical
unitary channels using multi-partite entanglement. We examine whether it is
possible for the rate at which the mean square error decreases to be greater
than that using the channels individually. For a reasonably general situation,
in which there is no functional dependence between the channels, we show that
this is not possible. We look at a case in which the channels are not
necessarily identical but depend on a common variable. In this case, the mean
square error decreases more rapidly using multi-partite entanglement.
