The DOI matches its Crossref record; 52 of the 52 references it cites were found in a registry or an index.
Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities
Open accessAbstract
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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Cites
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Self-testing of quantum systems: a review
Šupić, I., & Bowles, J. (2020) · Quantum · doi:10.22331/q-2020-09-30-337 · Cited by 365
All pure bipartite entangled states can be self-tested
Coladangelo, A., Goh, K. T., & Scarani, V. (2017) · Nature Communications · doi:10.1038/ncomms15485 · Cited by 205
Quantum fidelity measures for mixed states
Liang, Y.-C., Yeh, Y.-H., Mendonça, P. E. M. F., Teh, R. Y., Reid, M. D., & Drummond, P. D. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab1ca4 · Cited by 203
Self-testing quantum states and measurements in the prepare-and-measure scenario
Tavakoli, A., Kaniewski, J., Vértesi, T., Rosset, D., & Brunner, N. (2018) · Physical Review A · doi:10.1103/physreva.98.062307 · Cited by 121
Self-testing of binary observables based on commutation
Kaniewski, J. (2017) · Physical Review A · doi:10.1103/physreva.95.062323 · Cited by 96
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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