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Complete monogamy of multipartite quantum mutual information

Yu Guo1,* and Lizhong Huang2

  • 1School of Mathematical Sciences, Inner Mongolia University, Hohhot, Inner Mongolia 010021, People's Republic of China
  • 2Institute of Quantum Information Science, Shanxi Datong University, Datong, Shanxi 037009, People's Republic of China

  • *guoyu3@aliyun.com
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Phys. Rev. A 107, 042409 – Published 7 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042409

Abstract

Quantum mutual information not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here two alternatives of the multipartite quantum mutual information (MQMI) based on the von Neumann entropy according to the framework of the complete measure of the multiparticle quantum system. We show that these two MQMIs are complete and are monogamous on pure states, and one of them (we call it type-1) is not only completely monogamous but also tightly complete monogamous, while the other one (we call it type-2) is not. Moreover, we present another two MQMIs by replacing the von Neumann entropy with the Tsallis q-entropy from the former two ones. It is proved that one of them displays some degree of “completeness” as a measure of the multiparticle quantum system, but the other one is not even non-negative and thus it cannot be an alternative of MQMI. We also discuss the triangle relation for these three alternatives of MQMI. It is shown that the triangle inequalities hold for the former two MQMIs as that of entanglement measure but the later one fails. We thus can conclude that the type-1 von Neumann entropy MQMI is a “fine” measure of multipartite quantum correlation.

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Phys. Rev. A 107, 042409– Published 7 April, 2023
  • Received 24 November 2022
  • Accepted 24 March 2023
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