Reliable Interval Estimation for the Fidelity of Entangled States in Scenarios with General Noise

TL;DR

This paper introduces a method combining random sampling, a thought experiment, and Bayesian inference to accurately estimate the fidelity of entangled states in quantum networks affected by complex noise, providing reliable credible intervals.

Contribution

It presents a novel approach for fidelity estimation that accounts for general noise, improving accuracy and reliability over existing methods.

Findings

The credible interval effectively captures fidelity uncertainty under complex noise.

Proper measurement ratio is crucial for accurate fidelity estimation.

The method enhances confidence in quantum network quality control.

Abstract

Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to excessive uncertainty in the estimated fidelity. In this paper, the uncertainty associated with the estimated fidelity under conditions of general noise is constrained by jointly employing random sampling, a thought experiment, and Bayesian inference, resulting in a credible interval for fidelity that is valid in the presence of general noise. The proposed credible interval incorporates all even moments of the posterior distribution to enhance estimation accuracy. Factors influencing the estimation accuracy are identified and analyzed. Specifically, the issue of excessive measurements is addressed, emphasizing the necessity of properly determining the measurement ratio for fidelity estimation under general noise conditions.