  We revisit the problem of discriminating orthogonal quantum states within the
local quantum operation and classical communication (LOCC) paradigm. Our
particular focus is on the asymptotic situation where the parties have infinite
resources and the protocol may become arbitrarily long. Our main result is a
necessary condition for perfect asymptotic LOCC discrimination. As an
application, we prove that for complete product bases, unlimited resources are
of no advantage. On the other hand, we identify an example, for which it still
remains undecided whether unlimited resources are superior.
