Probing the robustness of various self-testing protocols for mulipartite entangled states
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| Format: | Preprint |
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2026
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| _version_ | 1866914530572894208 |
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| author | Jha, Priyaranjan K. Singh, Ritesh K. Pan, A. K. |
| author_facet | Jha, Priyaranjan K. Singh, Ritesh K. Pan, A. K. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probing the robustness of various self-testing protocols for mulipartite entangled states Jha, Priyaranjan K. Singh, Ritesh K. Pan, A. K. Quantum Physics 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. |
| title | Probing the robustness of various self-testing protocols for mulipartite entangled states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.03518 |