An alternative quantum fidelity for mixed states of qudits

TL;DR

This paper introduces a new, computationally efficient quantum fidelity measure for mixed states of qudits, based on Hilbert-Schmidt inner product and purity, satisfying key axioms.

Contribution

It proposes an alternative quantum fidelity definition that is easier to compute and adheres to established axioms, improving practical applicability.

Findings

The new fidelity measure satisfies Jozsa's axioms up to normalization.

It is computationally less demanding than existing measures.

The measure is well-defined for mixed states of qudits.

Abstract

We give an alternative definition of quantum fidelity for two density operators on qudits in terms of the Hilbert-Schmidt inner product between them and their purity. It can be regarded as the well-defined operator fidelity for the two operators and satisfies all Jozsa's four axioms up to a normalization factor. One desire property is that it is not computationally demanding.