Class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication

We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\mathcal{H}$, of any number of parties. Restricting consideration to measurements that act only on $\mathcal{H}$, 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 $\mathcal{H}$, then any LOCC measurement on an enlarged Hilbert space is effectively identical to an LOCC measurement on $\mathcal{H}$. 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.