# Probing the robustness of various self-testing protocols for multipartite entangled states

Source: [Probing the robustness of various self-testing protocols for multipartite entangled states](<https://www.sota2.com/research/paper/69facb3fc0f56ed84308a594>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-30T05:00:06.192Z

Authors: Priyaranjan K. Jha, Ritesh K. Singh, A. K. Pan

Published: 2026-05-05T08:55:46.000Z

## Abstract

Device-independent certification of multipartite entangled states plays a central role   in a wide range of practical applications, including quantum networks, conference key agreement, and verifiable distributed quantum computation. A particularly important class of multipartite entangled states is the class of Greenberger-Horne-Zeilinger (GHZ) states. Many Bell operators have been proposed to self-test GHZ states. However, in practical scenarios, due to imperfections and the finite collection of statistics, the observed statistics do not satisfy the ideal self-testing relations. Hence, it becomes essential to investigate and compare the robustness of the different self-testing protocols. In this work, we investigate the robustness of self-testing schemes constructed from Bell operators due to Svetlichny and Mermin--Ardehali--Belinskii--Klyshko (MABK), using the analytic operator-inequality framework developed by Kaniewski \[\\href{https://doi.org/10.1103/PhysRevLett.117.070402}{Phys. Rev. Lett. 117, 070402 (2016)}\]. We derive lower bounds on the extractable fidelity as a function of the observed value of these Bell operators. Although these protocols self-test the same underlying state, they exhibit markedly different levels of robustness. By comparing the resulting fidelity bounds, we demonstrate that the self-testing scheme based on the Svetlichny's Bell operator is the more robust among the two. Our results thus identify the Svetlichny operator based self-testing protocol as the most favorable candidate for device-independent certification of GHZ states in realistic, noisy experimental scenarios.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.03518>)

[PDF](<https://arxiv.org/pdf/2605.03518.pdf>)