Certifiable quantum dice: or, true random number generation secure against quantum adversaries
Open accessAbstract
We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n bits that are ε-close in statistical distance from n uniformly distributed bits, starting from a seed of O(log n log 1/ε) uniform bits. The bits generated are certifiably random based only on a simple statistical test that can be performed by the user, and on the assumption that the devices do not communicate in the middle of each phase of the protocol. No other assumptions are placed on the devices' inner workings. A modified protocol uses a seed of O(log3 n) uniformly random bits to generate n bits that are poly-1(n)-indistinguishable from uniform even from the point of view of a quantum adversary who may have had prior access to the devices, and may be entangled with them.
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A more sophisticated exponential randomness expansion protocol based on the CHSH inequality was proposed by Vidick and Vazirani, in which the length of the input seed is O(log2 n).
“A more sophisticated exponential randomness expansion protocol based on the CHSH inequality was proposed by Vidick and Vazirani, 59 in which the lengths of the input seed is O (log2 n ).”
From Quantum random number generation (2016) · cites this paper as [59]
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- Authors
- Vazirani, U., & Vidick, T.
- Affiliations
- US Berkeley, Berkeley, USA
- Massachusetts Institute of Technology (US)
- ORCID
- Vidick, Thomas
- Venue
- Proceedings of the forty-fourth annual ACM symposium on Theory of computing
- Publisher
- ACM
- Published
- 2012-05-19
- Pages
- 61-76
- OpenAlex
- W1967872567
- Cited by
- 80
- References
- 32
- Citations by year
- 2026: 4 · 2025: 1 · 2024: 2 · 2023: 1 · 2022: 3 · 2021: 9 · 2020: 6 · 2019: 8 · 2018: 8 · 2017: 5 · 2016: 11 · 2015: 4 · 2014: 12 · 2013: 4 · 2012: 2
- FWCI
- 5.40
- Type
- conference paper
- Language
- en
- Open access
- Locations
- ACM Symposium on Theory of Computing (STOC) (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- Funders
- National Science Foundation (0905626)
- Army Research Office (CCF-0905626, W911NF-09-1-0440, W911NF)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptography and Data Security
- Keywords
- quantum random number generation, certified randomness, randomness extraction, statistical distance, quantum adversaries, entanglement, device-independent randomness
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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