New entropic inequalities for qudit(spin j=9/2)

TL;DR

This paper derives new entropic inequalities for a single qudit system with spin j=9/2, revealing quantum hidden correlations and expanding the understanding of information measures in noncomposite quantum systems.

Contribution

It introduces novel entropic inequalities for a noncomposite qudit system, extending entropic property analysis beyond bipartite and tripartite systems.

Findings

Proved new entropic inequalities for spin j=9/2 qudit.

Demonstrated quantum hidden correlations in single qudit systems.

Analyzed von Neumann information as a function of a parameter.

Abstract

We consider information characteristics of single qudit state (spin j=9/2), such as von Neumann entropy, von Neumann mutual information. We review different mathematical properties of these information characteristics: subadditivity and strong subadditivity conditions, Araki-Lieb inequality. The inequalities are entropic inequalities for composite systems (bipartite, tripartite), but they can be written for noncomposite systems. Using the density matrix, describing the noncomposite qudit system state in explicit matrix form we proved new entropic inequalities for single qudit state (spin j=9/2). In addition, we also consider the von Neumann information of a qudit toy model as a function of a real parameter. The obtained inequalities describe the quantum hidden correlations in the single qudit system.