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Security of practical private randomness generation
Open accessAbstract
Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private; i.e., they appear random not only to the user but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed to sample the behavior of the quantum devices and to extract uniform randomness from the raw outputs of the devices, one usually speaks of device-independent randomness expansion. The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical side information; i.e., proving randomness against quantum side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, however, will generate cryptographically secure randomness that cannot be predicted by the adversary, and thus one can, given access to free public randomness, talk about private randomness generation. The theoretical tools to quantify the generated randomness according to these criteria were already introduced in S. Pironio et al. [Nature (London) 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device-independent randomness generation.
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“On the basis of the Clauser -Horne -Shimony -Holt (CHSH) inequality, 56 Fehr et al. 57 and Pironio et al. 58 proposed self-testing randomness expansion protocols against classical adversaries.”
From Quantum random number generation (2016) · cites this paper as [58]
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Metadata
- Authors
- Pironio, S., & Massar, S.
- Affiliations
- Université Libre de Bruxelles (BE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2013-01-30
- Volume
- 87
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1988732892
- Cited by
- 169
- References
- 48
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 6 · 2023: 10 · 2022: 4 · 2021: 12 · 2020: 18 · 2019: 38 · 2018: 12 · 2017: 7 · 2016: 9 · 2015: 10 · 2014: 12 · 2013: 13
- FWCI
- 16.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Agence Nationale de la Recherche (ANR-11-CHRI-0007)
- 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 › Computer Networks and Communications › Cryptography and Data Security
- Keywords
- device-independent randomness generation, private randomness, Bell inequality violation, randomness extraction
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