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arXiv:2512.06650

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

Zherui Jerry Wang, Joshua Carlo A. Casapao, Naphan Benchasattabuse, Ananda G. Maity, Jordi Tura, Akihito Soeda, Michal Hajdušek, Rodney Van Meter, David Elkouss

quant-phSubmitted Dec 7, 2025• Announced Dec 9, 2025• 0 citations
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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.

Comments
21 pages, 7 figures; comments welcome!

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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 (O(n)\mathcal{O}(n)O(n)), providing an exponential reduction in resource overhead compared to the best known O(2n)\mathcal{O}(2^n)O(2n) 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.
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Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic nnn-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all nnn-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.