Imaginarity measures induced by relative entropy

TL;DR

This paper introduces two new measures for quantifying imaginarity in quantum states, based on relative entropy concepts, and explores their relationships and properties within the resource theory framework.

Contribution

It presents novel imaginarity measures derived from $ ext{α}$--$ ext{z}$--Rényi and Tsallis relative entropies, expanding the tools for resource theory analysis.

Findings

The measures are well-defined for positive definite density matrices.

Relationships between different imaginarity measures are established.

Properties of the measures are analyzed within the resource theory context.

Abstract

In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by $\alpha$--$z$--R\'enyi relative entropy and the other, defined for positive definite density matrices, is induced by Tsallis relative operator entropy. The relationships between different imaginarity measures and their properties are also discussed.