Upper bounds for relative entropy of entanglement based on active learning

TL;DR

This paper introduces a machine learning approach using active learning to estimate upper bounds of the relative entropy of entanglement, enhancing entanglement quantification in quantum information theory.

Contribution

It presents a novel method leveraging active learning to approximate the set of separable states for calculating upper bounds of entanglement measures.

Findings

The method provides promising upper bounds for various quantum systems.

It improves upon previous lower bounds, offering a more complete picture of entanglement.

The approach deepens understanding of the structure of separable states.

Abstract

Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of $E_R$ were previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of $E_R$ based on active learning, a subfield in machine learning, to generate an approximation of the set of separable states. We apply our method to calculate $E_R$ for composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a reliable tool for entanglement measure calculation and deepens our understanding for the structure of separable states.