Conditions for local transformations between sets of quantum states

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.

Automated summary

In this study, we investigate the problem of transforming pure bipartite states using deterministic LOCC. We derive necessary conditions for such a transformation and classify all possible input-output pairs accordingly. Moreover, we prove strict inclusions between LOCC, separable, and positive partial transpose operations in set transformation problems.