  Quantum state discrimination involves identifying a given state out of a set
of possible states. When the states are mutually orthogonal, perfect state
discrimination is always possible using a global measurement. In the case of
multipartite systems when the parties are constrained to use multiple rounds of
local operations and classical communication (LOCC), perfect state
discrimination is often impossible even with the use of \emph{asymptotic LOCC},
wherein an error is allowed but must vanish in the limit of an infinite number
of rounds. Utilizing our recent results on asymptotic LOCC, we derive a lower
bound on the error probability for LOCC discrimination of any given set of
mutually orthogonal pure states. Informed by the insights gained from this
lower bound, we are able to prove necessary conditions for perfect state
discrimination by asymptotic LOCC. We then illustrate by example the power of
these necessary conditions in significantly simplifying the determination of
whether perfect discrimination of a given set of states can be accomplished
arbitrarily closely using LOCC. The latter examples include a proof that
perfect discrimination by asymptotic LOCC is impossible for a certain subset of
\emph{minimal} unextendible product bases (UPB), where minimal means that for
the given multipartite system, no UPB with a smaller number of states can
exist. We also give a simple proof that what has been called \emph{strong
nonlocality without entanglement} is considerably stronger than had previously
been demonstrated.
