Distribution of spin correlation strengths in multipartite systems

TL;DR

This paper extends the concept of isotropic spin correlation strength from two-qubit to multipartite qudit systems, deriving bounds, trade-offs, and monogamy relations, and analyzing their connection to quantum entanglement.

Contribution

It introduces a generalized measure of isotropic strength for multipartite qudit systems and establishes new bounds and relations, including monogamy-like constraints.

Findings

Sum of isotropic strengths in d-dimensional systems cannot exceed d-1

Derived trade-off and monogamy-like relations for tripartite and quadripartite systems

Boundaries of spin correlation strengths help analyze quantum entanglement

Abstract

For a two-qubit state the isotropic strength measures the degree of isotropic spin correlation. The concept of isotropic strength is generalized to multipartite qudit systems, and the strength distributions for tripartite and quadripartite qudit systems are thoroughly investigated. We show that the sum of relative isotropic strengths of any three qudit state over $d$-dimensional Hilbert space cannot exceed $d-1$, which generalizes of the case $d=2$. The trade-off relations and monogamy-like relations of the sum of spin correlation strengths for pure three- and four-partite systems are derived. Moreover, the bounds of spin correlation strengths among different subsystems of a quadripartite state are used to analyze quantum entanglement.