  We prove limitations on LOCC and separable measurements in bipartite state
discrimination problems using techniques from convex optimization. Specific
results that we prove include: an exact formula for the optimal probability of
correctly discriminating any set of either three or four Bell states via LOCC
or separable measurements when the parties are given an ancillary partially
entangled pair of qubits; an easily checkable characterization of when an
unextendable product set is perfectly discriminated by separable measurements,
along with the first known example of an unextendable product set that cannot
be perfectly discriminated by separable measurements; and an optimal bound on
the success probability for any LOCC or separable measurement for the recently
proposed state discrimination problem of Yu, Duan, and Ying.
