  We consider bipartite LOCC, the class of operations implementable by local
quantum operations and classical communication between two parties.
Surprisingly, there are operations that cannot be implemented with finitely
many messages but can be approximated to arbitrary precision with more and more
messages. This significantly complicates the analysis of what can or cannot be
approximated with LOCC. Towards alleviating this problem, we exhibit two
scenarios in which allowing vanishing error does not help. The first scenario
involves implementation of measurements with projective product measurement
operators. The second scenario is the discrimination of unextendible product
bases on two 3-dimensional systems.
