A lower bound on the fidelity between two states in terms of their trace-distance and max-relative entropy

TL;DR

This paper establishes a new lower bound on quantum fidelity using trace-norm distance and max-relative entropy, enhancing understanding of quantum state similarity measures.

Contribution

It introduces a novel lower bound on quantum fidelity based on trace-distance and max-relative entropy, expanding theoretical tools in quantum information.

Findings

Derived a lower bound on quantum fidelity involving trace-norm distance and max-relative entropy.

Provides theoretical insights into quantum state comparison metrics.

Enhances the mathematical framework for quantum information theory.

Abstract

Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two states in terms of their trace-norm distance and their max-relative entropy.