University of Oulu

Yanying Liang, Zhu-Jun Zheng, and Chuan-Jie Zhu, Phys. Rev. A 102, 062428 – Published 28 December 2020

Monogamy and polygamy for generalized W-class states using Renyi-alpha entropy

Saved in:
Author: Liang, Yanying1,2; Zheng, Zhu-Jun1,3; Zhu, Chuan-Jie4
Organizations: 1School of Mathematics, South China University of Technology, Guangzhou 510641, China
2Center for Machine Vision and Signal Analysis, University of Oulu, Oulu 90570, Finland
3Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou 510641, China
4College of Mathematics and Physics Science, Hunan University of Arts and Science, Changde 415000, People’s Republic of China
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.6 MB)
Persistent link:
Language: English
Published: American Physical Society, 2020
Publish Date: 2021-02-12


Monogamy of entanglement is an indispensable feature in multipartite quantum systems. In this paper we investigate monogamy and polygamy relations with respect to any partition for generalized W-class states using Rényi-α entropy. First, we present analytical formulas of Rényi-α entanglement (RαE) and Rényi-α entanglement of assistance (RαEoA) for a reduced density matrix of an n-qudit pure state in a superposition of generalized W-class states and vacuum. Based on the analytical formulas, we show monogamy and polygamy relations in terms of RαE and RαEoA. Next a reciprocal relation of RαEoA in an arbitrary three-party quantum system is found. Later, we further develop tighter monogamy relations in terms of concurrence and convex-roof extended negativity than former ones. In order to show the usefulness of our results, two partition-dependent residual entanglements are established to get a comprehensive analysis of entanglement dynamics for generalized W-class states. Moreover, we apply our results to an interesting quantum game and find a bound of the difference between the quantum game and the classical game.

see all

Series: Physical review. A
ISSN: 2469-9926
ISSN-E: 2469-9934
ISSN-L: 2469-9926
Volume: 102
Issue: 6
Article number: 062428
DOI: 10.1103/PhysRevA.102.062428
Type of Publication: A1 Journal article – refereed
Field of Science: 114 Physical sciences
Funding: This work is supported by the National Natural Science Foundation of China under Grant No. 11571119, the Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B1515310016, the Key Research and Development project of Guangdong Province under Grant No. 2020B0303300001, and the Chinese Scholarship Council.
Copyright information: © 2020 American Physical Society.