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Certifying the Dimension of Classical and Quantum Systems in a Prepare-and-Measure Scenario with Independent Devices
Open accessAbstract
We consider the problem of testing the dimension of uncharacterized classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem nonconvex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.
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“A positive value of this dimension witness could certify randomness in this scenario, similar to the fact that a violation of the Bell inequality could certify randomness of self-testing QRNG in Section ' Self-testing QRNG ' .”
From Quantum random number generation (2016) · cites this paper as [86]
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“The randomness can be estimated by adopting a dimension witness. 86”
From Quantum random number generation (2016) · cites this paper as [86]
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Cites
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Self-citationSemi-device-independent security of one-way quantum key distribution
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Self-citationDevice-Independent Tests of Classical and Quantum Dimensions
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Self-citationCharacterizing the Nonlocal Correlations Created via Entanglement Swapping
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Self-citationDimension Witnesses and Quantum State Discrimination
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Self-citationExperimental device-independent tests of classical and quantum dimensions
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Research works printed but not linked: 1
- J. Pearl, 2000, Models, Reasoning and Inference
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Quantum random number generators
Herrero-Collantes, M., & García-Escartín, J. C. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015004 · Cited by 850
“…QRNG of (Lunghi et al., 2015) where randomness from a quantum origin is separated from technical noise using the 31 dimension witness of (Bowles et al., 2014) defined as W = ∣∣∣∣∣ p (1 | 0, 0) − p (1 | 1, 0) p (1 | 2, 0) − p (1 | 3, 0) p (1 | 0, 1) − p (1 | 1, 1) p (1 | 2, 1) − p (1 |…”
Quantum random number generation
Ma, X., Yuan, X., Cao, Z., Qi, B., & Zhang, Z. (2016) · npj Quantum Information · doi:10.1038/npjqi.2016.21 · Cited by 445
“The randomness can be estimated by adopting a dimension witness.(86) A positive value of this dimension witness could certify randomness in this scenario, similar to the fact that a violation of the Bell inequality could certify randomness of self-testing QRNG in Section ‘Self-testing QRNG’.”
Self-testing of quantum systems: a review
Šupić, I., & Bowles, J. (2020) · Quantum · doi:10.22331/q-2020-09-30-337 · Cited by 365
Self-citationCertified randomness in quantum physics
Acín, A., & Masanes, L. (2016) · Nature · doi:10.1038/nature20119 · Cited by 307
“A solution to this problem was suggested in [68], where it was shown that schemes in which one assumes that the preparation and measuring device share no correlations, and that devices do not display memory effects, certify the presence of randomness for any value of the detection efficiency .”
BackgroundSelf-Testing Quantum Random Number Generator
Lunghi, T., Brask, J. B., Lim, C. C. W., Lavigne, Q., Bowles, J., Martin, A., Zbinden, H., & Brunner, N. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.150501 · Cited by 206
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Metadata
- Authors
- Bowles, J., Quintino, M. T., & Brunner, N.
- Affiliations
- University of Geneva (CH)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2014-04-11
- Volume
- 112
- Issue
- 14
- Pages
- 140407-140407
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2070059557
- Cited by
- 116
- References
- 22
- Citations by year
- 2026: 7 · 2025: 4 · 2024: 13 · 2023: 16 · 2022: 7 · 2021: 13 · 2020: 13 · 2019: 9 · 2018: 5 · 2017: 9 · 2016: 10 · 2015: 8 · 2014: 1
- FWCI
- 9.30
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Archive ouverte UNIGE (University of Geneva) (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- Archive ouverte UNIGE (University of Geneva) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- National Science Foundation (PP00P2_138917)
- 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
- dimension witness, prepare-and-measure scenario, noise robustness, randomness certification, non-convex optimization
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