New inequality for density matrices of single qudit states

TL;DR

This paper derives new entropic inequalities for single qudit density matrices using the monotonicity of relative entropy, providing explicit bounds and examples for qutrit states and their distances.

Contribution

It introduces novel entropic inequalities for single qudit states based on relative entropy monotonicity, with explicit examples for qutrits and state distance bounds.

Findings

New entropic inequalities for qudit density matrices

Explicit bounds for qutrit state distances

Illustrative examples for qutrit and qubit states

Abstract

Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the distance between the qutrit states are considered in explicit form.