Two imaginarity monotones induced by unified $(\alpha,\beta)$-relative entropy

TL;DR

This paper introduces two new imaginarity monotones based on the unified $(eta,eta)$-relative entropy, advancing the resource theory of imaginarity in quantum mechanics by analyzing their properties and providing illustrative examples.

Contribution

The paper proposes novel imaginarity monotones derived from the unified $(eta,eta)$-relative entropy, enriching the mathematical framework of imaginarity resource theory.

Findings

Two types of imaginarity monotones are defined and analyzed.

Properties of the monotones are systematically investigated.

Explicit examples demonstrate the application of the proposed monotones.

Abstract

Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified $(\alpha,\beta)$-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.