Spectral Graph Theoretic Analysis of Tsallis Entropy-based Dissimilarity Measure

TL;DR

This paper introduces a novel spectral graph-theoretic measure based on Tsallis entropy for quantum information, which is symmetric, convex, and applicable to multiple density matrices with weighted options.

Contribution

It presents a new nonextensive quantum divergence measure that is symmetric, matrix-convex, and generalizable to multiple density matrices, expanding quantum information analysis tools.

Findings

The measure is symmetric and matrix-convex.

It is theoretically upper-bounded.

Applicable to any number of density matrices with weighting options.

Abstract

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework. Unlike other entropic measures, the proposed quantum divergence is symmetric, matrix-convex, theoretically upper-bounded, and has the advantage of being generalizable to any arbitrary number of density matrices, with a possibility of assigning weights to these densities.