Bound on trace distance based on superfidelity

TL;DR

This paper introduces a new bound on the trace distance between quantum states using superfidelity, which can be estimated efficiently and offers advantages over existing fidelity-based bounds.

Contribution

The paper presents a novel trace distance bound based on superfidelity, simplifying estimation and comparison with traditional fidelity-based bounds.

Findings

The superfidelity-based bound is easier to estimate experimentally.

The new bound provides a tighter estimate in certain quantum state comparisons.

Comparison shows advantages over existing fidelity-based bounds.

Abstract

We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be estimated using a simple measurement procedure. We also compare this bound with the one provided in terms of fidelity.