Unified (r,s)-relative entropy

TL;DR

This paper introduces a new unified $(r,s)$-relative entropy concept for quantum states, explores its properties on separable Hilbert spaces, and examines its application as an entanglement measure, correcting previous monotonicity issues.

Contribution

It presents the first study of unified $(r,s)$-relative entropy in quantum information, including its properties and role as an entanglement measure, with improvements over prior monotonicity claims.

Findings

Defined quantum unified $(r,s)$-relative entropy on separable Hilbert spaces

Analyzed the entanglement-measure properties of the new entropy

Corrected previous inaccuracies regarding monotone properties

Abstract

In this paper, we introduce and study unified $(r,s)$-relative entropy and quantum unified $(r,s)$-relative entropy, in particular, our main results of quantum unified $(r,s)$-relative entropy are established on the separable complex Hilbert spaces. Moreover, the entanglement-measure of states due to the quantum unified $(r,s)$-relative entropy is considered, too. Our results improved a uncorrect statement on the monotone property of entanglement-measure function.