Error minimization for fidelity estimation of GHZ states with arbitrary noise

TL;DR

This paper introduces a new fidelity estimation protocol for noisy GHZ states that minimizes mean squared error, works under arbitrary noise without prior info, and uses only local measurements, outperforming existing methods.

Contribution

It develops a fidelity-preserving diagonalization and Fisher information maximization approach for optimal estimation under arbitrary noise without prior knowledge.

Findings

Reduces estimation errors compared to existing protocols.

Effective under both i.i.d. and correlated noise.

Uses only local Pauli measurements for implementation.

Abstract

Fidelity estimation is a crucial component for the quality control of entanglement distribution networks. This work studies a scenario in which multiple nodes share noisy Greenberger-Horne-Zeilinger (GHZ) states. Due to the collapsing nature of quantum measurements, the nodes randomly sample a subset of noisy GHZ states for measurement and then estimate the average fidelity of the unsampled states conditioned on the measurement outcome. By developing a fidelity-preserving diagonalization operation, analyzing the Bloch representation of GHZ states, and maximizing the Fisher information, the proposed estimation protocol achieves the minimum mean squared estimation error in a challenging scenario characterized by arbitrary noise and the absence of prior information. Additionally, this protocol is implementation-friendly as it only uses local Pauli operators according to a predefined sequence. Numerical studies demonstrate that, compared to existing fidelity estimation protocols, the proposed protocol reduces estimation errors in both scenarios involving independent and identically distributed (i.i.d.) noise and correlated noise.