Upper bounds for relative entropy of entanglement based on active learning. (17th September 2020)

• Record Type: Journal Article
• Authors: Hou, Shi-Yao; Cao, Chenfeng; Zhou, D L; Zeng, Bei
• Is Part Of: Quantum science and technology. Volume 5:Number 4(2020)
• Publication Date: 2020-09-17
• Subjects: relative entropy of entanglement -- active learning -- upper bound -- convex hull approximation; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/abb412
• Languages: English
• ISSNs: 2058-9565

Abstract

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.