Fidelity as a figure of merit in quantum error correction

TL;DR

This paper examines the limitations of using fidelity as a figure of merit in quantum error correction, highlighting that optimizing fidelity may not always preserve mutual information and may overlook critical error details.

Contribution

The paper critically analyzes the use of fidelity in quantum error correction, showing it can be misleading and proposing the need for alternative metrics that better preserve information.

Findings

Fidelity may decrease mutual information when correcting uncorrectable errors.

Optimizing fidelity can overlook the importance of error localization.

Fidelity is not always the best figure of merit for quantum information integrity.

Abstract

We discuss the fidelity as a figure of merit in quantum error correction schemes. We show that when identifiable but uncorrectable errors occur as a result of the action of the channel, a common strategy that improves the fidelity actually decreases the transmitted mutual information. The conclusion is that while the fidelity is simple to calculate and therefore often used, it is perhaps not always a recommendable figure of merit for quantum error correction. The reason is that while it roughly speaking encourages optimisation of the "mean probability of success", it gives no incentive for a protocol to indicate exactly where the errors lurk. For small error probabilities, the latter information is more important for the integrity of the information than optimising the mean probability of success.