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Simple and tight device-independent security proofs

Arnon-Friedman, Rotem and Renner, Renato and Vidick, Thomas (2019) Simple and tight device-independent security proofs. SIAM Journal on Computing, 48 (1). pp. 181-225. ISSN 0097-5397. http://resolver.caltech.edu/CaltechAUTHORS:20190206-150209557

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Abstract

Device-independent security is the gold standard for quantum cryptography: not only is security based entirely on the laws of quantum mechanics, but it holds irrespective of any a priori assumptions on the quantum devices used in a protocol, making it particularly applicable in a quantum-wary environment. While the existence of device-independent protocols for tasks such as randomness expansion and quantum key distribution has recently been established, the underlying proofs of security remain very challenging, yield rather poor key rates, and demand very high quality quantum devices, thus making them all but impossible to implement in practice. We introduce a technique for the analysis of device-independent cryptographic protocols. We provide a flexible protocol and give a security proof that provides quantitative bounds that are asymptotically tight, even in the presence of general quantum adversaries. At a high level our approach amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This is achieved by leveraging the sequential nature of the protocol and makes use of a newly developed tool, the “entropy accumulation theorem” of Dupuis, Fawzi, and Renner [Entropy Accumulation, preprint, 2016]. As concrete applications we give simple and modular security proofs for device-independent quantum key distribution and randomness expansion protocols based on the CHSH inequality. For both tasks, we establish essentially optimal asymptotic key rates and noise tolerance. In view of recent experimental progress, which has culminated in loophole-free Bell tests, it is likely that these protocols can be practically implemented in the near future.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/18M1174726DOIArticle
https://arxiv.org/abs/1607.01797arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2019 Society for Industrial and Applied Mathematics. Submitted: 9 March 2018; Accepted: 19 December 2018; Published online: 26 February 2019. The research of the first and second authors was supported by the Stellenbosch Institute for Advanced Study (STIAS), by the European Commission via the project "RAQUEL," by the Swiss National Science Foundation via the National Center for Competence in Research, QSIT, and by the Air Force Office of Scientific Research (AFOSR) via grant FA9550-16-1-0245. The third author's research was partially supported by NSF CAREER grant CCF-1553477, an AFOSR YIP award, the IQIM, and the NSF Physics Frontiers Center (NFS grant PHY-1125565) with support from the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Stellenbosch Institute for Advanced Study (STIAS)UNSPECIFIED
European Research Council (ERC)RAQUEL
Swiss National Science Foundation (SNSF)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0245
NSFCCF-1553477
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Subject Keywords:quantum cryptography, device independence, key distribution, security proofs, randomness
Classification Code:AMS subject classifications. 81P94, 81P45, 81P40, 94A60
Record Number:CaltechAUTHORS:20190206-150209557
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190206-150209557
Official Citation:Simple and Tight Device-Independent Security Proofs Rotem Arnon-Friedman, Renato Renner, and Thomas Vidick SIAM Journal on Computing 2019 48:1, 181-225; doi: 10.1137/18M1174726
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92744
Collection:CaltechAUTHORS
Deposited By: Bonnie Leung
Deposited On:07 Feb 2019 00:01
Last Modified:20 Mar 2019 23:27

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