Geometric interpretation for A-fidelity and its relation with Bures fidelity

TL;DR

This paper provides a geometric interpretation of A-fidelity for qubits, establishes an upper bound for Bures fidelity, and explores metric properties and generalizations to N-state systems.

Contribution

It introduces a geometric perspective for A-fidelity, derives an upper bound for Bures fidelity, and extends the concept to multi-state quantum systems.

Findings

A geometric interpretation of A-fidelity for qubits

An upper bound for Bures fidelity based on A-fidelity

A discussion on metrics and generalizations to N-state systems

Abstract

A geometric interpretation for the A-fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the A-fidelity are studied by numerical method. An alternative generalization of the A-fidelity, which has the same geometric picture, to a $N$-state quantum system is also discussed.