NDLI: Universal Security for Randomness Expansion from the Spot-Checking Protocol

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Shi, Yaoyun Miller, Carl A.
Copyright Year	2017
Abstract	Colbeck [Ph.D. thesis, 2006] proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves the known noise tolerance for secure randomness expansion: for the commonly used CHSH game, full security was only known with a noise tolerance of 1.5% [Miller and Shi, J. ACM, 63 (2016), 33], and we improve this to 10.3%. We also generalize our results beyond Bell inequalities and give the first security proof for randomness expansion based on Kochen--Specker inequalities. The central technical contribution of the paper is a new uncertainty principle for the Schatten norm, which is based on the uniform convexity inequality of Ball, Carlen, and Lieb [Invent. Math., 115 (1994), pp. 463--482].
Sponsorship	National Science Foundation
Starting Page	1304
Ending Page	1335
Page Count	32
File Format	PDF
ISSN	00975397
DOI	10.1137/15M1044333
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	46
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-08-01
Access Restriction	Subscribed
Subject Keyword	nonlocality Contextuality quantum cryptography Norms of matrices, numerical range, applications of functional analysis to matrix theory random number generation device-independence Quantum cryptography bell inequalities
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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