  We consider an infinite class of unambiguous quantum state discrimination
problems on multipartite systems, described by Hilbert space $\cal{H}$, of any
number of parties. Restricting consideration to measurements that act only on
$\cal{H}$, we find the optimal global measurement for each element of this
class, achieving the maximum possible success probability of $1/2$ in all
cases. This measurement turns out to be both separable and unique, and by our
recently discovered necessary condition for local quantum operations and
classical communication (LOCC), it is easily shown to be impossible by any
finite-round LOCC protocol. We also show that, quite generally, if the input
state is restricted to lie in $\cal{H}$, then any LOCC measurement on an
enlarged Hilbert space is effectively identical to an LOCC measurement on
$\cal{H}$. Therefore, our necessary condition for LOCC demonstrates directly
that a higher success probability is attainable for each of these problems
using general separable measurements as compared to that which is possible with
any finite-round LOCC protocol.
