Quantum fidelity measures for mixed states

TL;DR

This paper reviews various quantum fidelity measures for mixed states, comparing their properties and applications in quantum technologies, highlighting the diversity and suitability of different measures for practical quantum information tasks.

Contribution

It systematically compares and analyzes the properties of multiple quantum fidelity measures for mixed states, providing a comprehensive overview and criteria for their suitability.

Findings

Many fidelity measures satisfy key properties

Detailed proofs of measure properties are provided

Applications in teleportation, quantum memories, and more are summarized

Abstract

Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories, quantum computers, quantum communications, and quantum phase-space simulations.