Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
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Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance, observing the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality certifies that the two parties share a singlet. While self-testing results are known for several classes of states, in many cases they are only applicable if the observed statistics are almost perfect, which makes them unsuitable for practical applications. Practically relevant self-testing bounds are much less common and moreover they all result from a single numerical method (with one exception which we discuss in detail). In this work we present a new technique for proving analytic self-testing bounds of practically relevant robustness. We obtain improved bounds for the case of self-testing the singlet using the CHSH inequality (in particular we show that nontrivial fidelity with the singlet can be achieved as long as the violation exceeds β^{*}=(16+14sqrt[2])/17≈2.11). In the case of self-testing the tripartite Greenberger-Horne-Zeilinger state using the Mermin inequality, we derive a bound which not only improves on previously known results but turns out to be tight. We discuss other scenarios to which our technique can be immediately applied.
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Multipartite systems do not have fixed thresholds or strictly bounded metrics.
“whereas Bell’s inequality sets an experimental threshold of 2√2 and a theoretical threshold of √16 [56], [57], multipartite systems do not have fixed thresholds or strictly bounded metrics [32].”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [32]
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Li, J., Liu, T.-J., Wang, S., Jebarathinam, C., & Wang, Q. (2019) · Optics Express · doi:10.1364/oe.27.013559 · Cited by 13 · see citing works
Toward the Device-Independent Certification of a Quantum Memory.
Sekatski, P., Bancal, J., Ioannou, M., Afzelius, M., & Brunner, N. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.170802 · Cited by 13 · see citing works
Murta, G., & Baccari, F. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.140201 · Cited by 12 · see citing works
Robust Approach for Time-Bin-Encoded Photonic Quantum Information Protocols
White, S., Polino, E., Ghafari, F., Joch, D. J., Villegas-Aguilar, L., Shalm, L. K., Verma, V. B., Huber, M., & Tischler, N. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.180802 · Cited by 12 · see citing works
Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing.
Wu, D., Zhao, Q., Wang, C., Huang, L., Jiang, Y.-F., Bai, B., Zhou, Y., Gu, X.-M., Liu, F.-M., Mao, Y.-Q., et al. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.250401 · Cited by 10 · see citing works
Quantum correlations on the no-signaling boundary: self-testing and more
Chen, K.-S., Tabia, G. N. M., Jebarathinam, C., Mal, S., Wu, J.-Y., & Liang, Y.-C. (2023) · Quantum · doi:10.22331/q-2023-07-11-1054 · Cited by 12 · see citing works
Lee, S., Park, J., Kim, J., & Noh, C. (2017) · Physical Review A · doi:10.1103/physreva.95.012134 · Cited by 11 · see citing works
Near-Maximal Two-Photon Entanglement for Optical Quantum Communication at 2.1μm
Dada, A. C., Kaniewski, J., Gawith, C. B. E., Lavery, M. P. J., Hadfield, R. H., Faccio, D., & Clerici, M. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.16.l051005 · Cited by 11 · see citing works
What is the minimum CHSH score certifying that a state resembles the singlet?
Valcarce, X., Sekatski, P., Orsucci, D., Oudot, E., Bancal, J.-D., & Sangouard, N. (2020) · Quantum · doi:10.22331/q-2020-03-23-246 · Cited by 12 · see citing works
Zhang, C., Zhang, W.-H., Sekatski, P., Bancal, J., Zwerger, M., Yin, P., Li, G.-C., Peng, X.-X., Chen, L., Han, Y.-J., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.129.190503 · Cited by 5 · see citing works
Self-testing two-qubit maximally entangled states from generalized Clauser-Horne-Shimony-Holt tests
Valcarce, X., Zivy, J., Sangouard, N., & Sekatski, P. (2020) · Physical Review Research · doi:10.1103/physrevresearch.4.013049 · Cited by 9 · see citing works
Authenticated teleportation with one-sided trust
Unnikrishnan, A., & Markham, D. (2019) · Physical Review A · doi:10.1103/physreva.100.032314 · Cited by 9 · see citing works
Płodzień, M., Chwedeńczuk, J., Lewenstein, M., & Rajchel-Mieldzioć, G. (2024) · Physical Review A · doi:10.1103/physreva.110.032428 · Cited by 10 · see citing works
Complete Self-Testing of a System of Remote Superconducting Qubits
Storz, S., Kulikov, A., Schär, J., Barizien, V., Valcarce, X., Berterottière, F., Sangouard, N., Bancal, J.-D., & Wallraff, A. J. (2025) · Physical Review Letters · doi:10.1103/nv7d-k3wr · Cited by 11 · see citing works
Self-Testing of Symmetric Three-Qubit States
Li, X.-H., Wang, Y., Han, Y.-G., Qin, S.-J., Gao, F., & Wen, Q.-Y. (2019) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2020.2968994 · Cited by 8 · see citing works
Advances of Quantum Key Distribution and Network Nonlocality
Geng, M. (2025) · Entropy · doi:10.3390/e27090950 · Cited by 7 · see citing works
Analytic robustness bound for self-testing of the singlet with two binary measurements
Li, X., Wang, Y., Han, Y.-G., Qin, S., Gao, F., & Wen, Q. (2019) · Journal of the Optical Society of America B · doi:10.1364/josab.36.000457 · Cited by 7 · see citing works
Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses
Bierhorst, P., & Prakash, J. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.250201 · Cited by 7 · see citing works
Bell’s inequality, generalized concurrence and entanglement in qubits
Chang, P.-Y., Chu, S.-K., & Ma, C. (2019) · International Journal of Modern Physics A · doi:10.1142/s0217751x19500325 · Cited by 8 · see citing works
Scalable determination of multipartite entanglement in quantum networks
Kao, W., Huang, C.-Y., Tsai, T.-J., Chen, S.-H., Sun, S.-Y., Li, Y., Liao, T., Chuu, C., Lu, H., & Li, C. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00867-0 · Cited by 8 · see citing works
Device-independent quantum key distribution beyond qubits
Rivera-Dean, J., Steffinlongo, A., Parker-Sánchez, N., Acín, A., & Oudot, E. (2025) · New Journal of Physics · doi:10.1088/1367-2630/add8b3 · Cited by 6 · see citing works
Self-testing of genuine multipartite entangled states without network assistance
Adhikary, R., Mishra, A., & Rahaman, R. (2024) · Physical Review A · doi:10.1103/physreva.110.l010401 · Cited by 8 · see citing works
Paul, R., Sasmal, S., & Pan, A. K. (2024) · Physical Review A · doi:10.1103/physreva.110.012444 · Cited by 6 · see citing works
Quantifying unknown entanglement by neural networks
Lin, X., Chen, Z.-Y., & Wei, Z. (2021) · Quantum Information Processing · doi:10.1007/s11128-023-04068-0 · Cited by 5 · see citing works
Experimental self-testing for photonic graph states.
Xu, J.-M., Zhou, Q., Yang, Y.-X., Cheng, Z.-M., Xu, X.-Y., Ren, Z.-C., Wang, X.-L., & Wang, H.-T. (2021) · Optics Express · doi:10.1364/oe.446154 · Cited by 5 · see citing works
Experimental verification of a new Bell-type inequality
Zhao, J., Cao, L., Yang, Y., Li, Y., & Lu, H.-X. (2018) · Physics Letters A · doi:10.1016/j.physleta.2018.03.013 · Cited by 6 · see citing works
Escolà-Gascón, Á., & Benito-León, J. (2025) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2025.04.025 · Cited by 4 · see citing works
Constructing multipartite Bell inequalities from stabilizers
Zhao, Q., & Zhou, Y. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043215 · Cited by 5 · see citing works
Self-testing of different entanglement resources via fixed measurement settings
Li, X.-H., Wang, Y., Han, Y.-G., & Zhu, S.-R. (2022) · Physical Review A · doi:10.1103/physreva.106.052418 · Cited by 3 · see citing works
Bock, M., Sekatski, P., Bancal, J.-D., Kucera, S., Bauer, T., Sangouard, N., Becher, C., & Eschner, J. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00859-0 · Cited by 5 · see citing works
Device-independent characterizations of a shared quantum state independent of any Bell inequalities
Wei, Z., & Sikora, J. (2017) · Physical Review A · doi:10.1103/physreva.95.032103 · Cited by 5 · see citing works
Scalable noncontextuality inequalities and certification of multiqubit quantum systems
Santos, R., Jebarathinam, C., & Augusiak, R. (2022) · Physical Review A · doi:10.1103/physreva.106.012431 · Cited by 3 · see citing works
Machine-learning-based device-independent certification of quantum networks
D'Alessandro, N., Polacchi, B., Moreno, G., Polino, E., Chaves, R., Agresti, I., & Sciarrino, F. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023016 · Cited by 5 · see citing works
Experimental full calibration of quantum devices in a semi-device-independent way
Li, G.-C., Yin, Z., Zhang, W.-H., Chen, L., Yin, P., Peng, X.-X., Hong, X.-S., Chen, G., Li, C., & Guo, G. (2023) · Optica · doi:10.1364/optica.502274 · Cited by 5 · see citing works
Analytic semi-device-independent entanglement quantification for bipartite quantum states
Wei, Z., & Lin, L. (2021) · Physical Review A · doi:10.1103/physreva.103.032215 · Cited by 4 · see citing works
Self-testing of genuine multipartite non-local and non-maximally entangled states
Adhikary, R. (2024) · Physics Letters A · doi:10.1016/j.physleta.2024.129731 · Cited by 4 · see citing works
Experimental certification of nonprojective quantum measurements under a minimum overlap assumption
Fan, Q., Ma, M.-Y., Sun, Y.-N., Su, Q.-P., & Yang, C. (2022) · Optics Express · doi:10.1364/oe.469225 · Cited by 4 · see citing works
Wei, S.-H., Guo, F.-Z., Li, X., & Wen, Q. (2019) · Chinese Physics B · doi:10.1088/1674-1056/28/7/070304 · Cited by 4 · see citing works
Zhang, X., & Zhao, Q. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033400 · Cited by 4 · see citing works
Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game
Faleiro, R., & Goulão, M. (2021) · Physical Review A · doi:10.1103/physreva.103.022430 · Cited by 4 · see citing works
Singh, R. K., Sasmal, S., & Pan, A. K. (2025) · Physical Review A · doi:10.1103/x6ct-vmnx · Cited by 3 · see citing works
Self-guided method to search maximal Bell violations for unknown quantum states
Yang, L.-K., Chen, G., Zhang, W.-H., Peng, X.-X., Yu, S., Ye, X.-J., Li, C., & Guo, G. (2017) · Physical Review A · doi:10.1103/physreva.96.052310 · Cited by 3 · see citing works
Trusted quantum remote sensing based on self-testing of entangled states
Peng, X.-X., Zhang, W.-H., Yin, P., Li, G., Chen, L., Chen, G., Li, C., & Guo, G. (2022) · Physical Review A · doi:10.1103/physreva.105.032615 · Cited by 3 · see citing works
Gigena, N., & Kaniewski, J. (2022) · Physical Review A · doi:10.1103/physreva.106.012401
Nonlocal correlations in quantum networks distributed with different entangled states
Hsu, L. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad313c · Cited by 4 · see citing works
- Authors
- Kaniewski, J.
- Affiliations
- University of Copenhagen (DK)
- Corresponding author
- Kaniewski, Jędrzej
- ORCID
- Kaniewski, Jędrzej
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2016-08-11
- Volume
- 117
- Issue
- 7
- Pages
- 070402-070402
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2344582723
- Cited by
- 144
- References
- 52
- Citations by year
- 2026: 5 · 2025: 23 · 2024: 15 · 2023: 13 · 2022: 18 · 2021: 16 · 2020: 18 · 2019: 17 · 2018: 11 · 2017: 7 · 2016: 1
- FWCI
- 9.86
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- Research at the University of Copenhagen (University of Copenhagen) (publishedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- European Research Council (337603)
- Det Frie Forskningsråd
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (PP00P2_150734)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- self-testing, CHSH inequality, Mermin inequality, singlet state, GHZ states, quantum correlations, analytic bounds, robustness, device-independent quantum cryptography, quantum fidelity, Bell nonlocality
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