Conditions for local transformations between sets of quantum states

TL;DR

This paper investigates the conditions under which one set of pure bipartite quantum states can be deterministically transformed into another using LOCC, revealing necessary but not sufficient criteria and classifying possible transformations.

Contribution

It introduces necessary conditions for set transformations under LOCC, analyzes their independence, and distinguishes between LOCC, separable, and PPT operations in this context.

Findings

Necessary conditions are independent but not sufficient for transformations.

Classified all input-output pairs of state sets based on these conditions.

Proved strict inclusions between LOCC, separable, and PPT operations for set transformations.

Abstract

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.