Entanglement transformation between sets of bipartite pure quantum states using local operations

TL;DR

This paper establishes necessary and sufficient conditions for transforming sets of bipartite pure quantum states using local operations, and provides efficient algorithms to determine the feasibility of such transformations.

Contribution

It introduces a complete characterization of entanglement transformations between sets of pure states with practical algorithms for verification.

Findings

Derived necessary and sufficient conditions for state set transformations.

Developed efficient algorithms to test transformation feasibility.

Enhanced understanding of entanglement manipulation in quantum information.

Abstract

Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient conditions on the existence of such a transformation. We also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states.