Alternative fidelity measure for quantum states

TL;DR

This paper introduces a new, computationally simpler fidelity measure for quantum states that satisfies key axioms but has different mathematical properties, and explores related metrics and properties.

Contribution

It proposes an alternative fidelity measure based on linear entropy and Hilbert-Schmidt inner product, with unique properties and computational advantages.

Findings

The new measure is jointly concave and satisfies Jozsa's axioms.

It is supermultiplicative and not monotonic under quantum operations.

New metrics for density matrices are identified, and Uhlmann-Jozsa fidelity's concavity for qubits is established.

Abstract

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.