Quantifying the imaginarity of quantum states via Tsallis relative entropy

TL;DR

This paper introduces a new measure of quantum imaginarity based on Tsallis relative entropy, providing explicit formulas and computability for bosonic Gaussian states, advancing understanding of the role of complex numbers in quantum mechanics.

Contribution

It proposes a novel imaginarity measure using Tsallis relative entropy, with explicit expression and computability for bosonic Gaussian states, enriching the resource theory of quantum imaginarity.

Findings

The new measure is explicitly expressed and computable.

It applies specifically to bosonic Gaussian states.

Enhances understanding of quantum imaginarity and its quantification.

Abstract

It is a fundamental question that why quantum mechanics uses complex numbers instead of only real numbers. To address this topic, recently, a rigorous resource theory for the imaginarity of quantum states were established, and several imaginarity measures were proposed. In this work, we propose a new imaginarity measure based on the Tsallis relative entropy. This imaginarity measure has explicit expression, and also, it is computable for bosonic Gaussian states.