Tripartite entanglement measure under local operations and classical communication

作     者：Ge, Xiaozhen Liu, Lijun Cheng, Shuming 

作者机构：Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong College of Mathematics and Computer Science Shanxi Normal University Linfen041000 China The Department of Control Science and Engineering Tongji University Shanghai201804 China Shanghai Institute of Intelligent Science and Technology Tongji University Shanghai201804 China Institute for Advanced Study Tongji University Shanghai200092 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Quantum communication 

摘      要：Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system in [S. Xie et al., Phys. Rev. Lett. 127. 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC-monotonicity of three-tangle and find that the bipartite concurrence and the squared can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalised to the multipartite system. Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems. Copyright © 2022, The Authors. All rights reserved.