  We study the problem of transforming a set of pure bipartite states into
another using deterministic LOCC (local operations and classical
communication). Necessary conditions for the existence of such a transformation
are obtained using LOCC constraints on state transformation, entanglement, and
distinguishability. These conditions are shown to be independent but not
sufficient. We discuss their satisfiability and classify all possible
input-output pairs of sets accordingly. We also prove that strict inclusions
hold between LOCC, separable, and positive partial transpose operations for set
transformation problems.
