Complete monogamy of the multipartite quantum mutual information

TL;DR

This paper investigates different formulations of multipartite quantum mutual information, demonstrating their properties such as completeness and monogamy, and compares their effectiveness in characterizing quantum correlations.

Contribution

It introduces and analyzes multiple versions of multipartite quantum mutual information, establishing their monogamy properties and comparing their suitability for measuring quantum correlations.

Findings

Two MQMI are complete and monogamous on pure states.

One MQMI is tightly complete monogamous, the other is not.

Replacing von Neumann entropy with Tsallis q-entropy affects measure properties.

Abstract

Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information (MQMI) based on the von Neumann entropy according to the framework of the complete measure of multi-particle quantum system. We show that these two MQMI are complete, monogamous on pure states, and one of them is not only completely monogamous but also tightly complete monogamous while another one is not. Moreover, we present another two MQMI by replacing the von Neumann entropy with the Tasllis $q$-entropy from the former two ones. It is proved that one of them displays some degree of ``completeness'' as a measure of multi-particle quantum system, but the other one is not even non-negative and thus it can not be a 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 MQMI as that of entanglement measure but the later one fails. By comparison, we found that the von Neumann entropy is better than other versions of entropy as desired when we characterize the quantum correlation in multi-particle system.