  We study scenarios which arise when two spatially-separated observers, Alice
and Bob, are try to identify a quantum state sampled from several
possibilities. In particular, we examine their strategies for maximizing both
the probability of guessing their state correctly as well as their information
gain about it. It is known that there are scenarios where allowing Alice and
Bob to use LOCC offers an improvement over the case where they must make their
measurements simultaneously. Similarly, Alice and Bob can sometimes improve
their outcomes if they have access to a Bell pair. We show how LOCC allows
Alice and Bob to distinguish between two product states optimally and find that
a LOCC is almost always more helpful than a Bell pair for distinguishing
product states.
