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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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“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 Q statistical distribution in quantum consciousness modeling (2025) · cites this paper as [32]
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Singh, R. K., Sasmal, S., & Pan, A. K. (2025) · Physical Review A · doi:10.1103/x6ct-vmnx · Cited by 4
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
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
Quantum value for a family of I3322 -like Bell functionals
Gigena, N., & Kaniewski, J. (2022) · Physical Review A · doi:10.1103/physreva.106.012401 · Cited by 6
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
Metadata
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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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