Efficient graph-diagonal characterization of noisy states distributed over quantum networks via Bell sampling

TL;DR

This paper introduces a scalable Bell sampling protocol for efficiently characterizing noisy graph states in quantum networks, significantly reducing resource requirements compared to traditional methods.

Contribution

The authors develop a Bell sampling-based method that estimates diagonal elements of noisy graph states with linear sample complexity, outperforming previous exponential-scaling techniques.

Findings

Sample complexity scales linearly with the number of qubits

Global properties like fidelity can be estimated independently of network size

Numerical results show practical efficiency exceeds theoretical bounds

Abstract

Graph states are an important class of entangled states that serve as a key resource for distributed information processing and communication in quantum networks. In this work, we propose a protocol that utilizes a Bell sampling subroutine to characterize the diagonal elements in the graph basis of noisy graph states distributed across a network. Our approach offers significant advantages over direct diagonal estimation using unentangled single-qubit measurements in terms of scalability. Specifically, we prove that estimating the full vector of diagonal elements requires a sample complexity that scales linearly with the number of qubits ($\mathcal{O}(n)$), providing an exponential reduction in resource overhead compared to the best known $\mathcal{O}(2^n)$ scaling of direct estimation. Furthermore, we demonstrate that global properties, such as state fidelity, can be estimated with a sample complexity independent of the network size. Finally, we present numerical results indicating that the estimation in practice is more efficient than the derived theoretical bounds. Our work thus establishes a promising technique for efficiently estimating noisy graph states in large networks under realistic experimental conditions.