



01611nas a2200133   4500008004100000245008000041210006900121260001500190490000700205520118300212100001701395700001601412856004901428       2017                        eng d00aUniversal Security for Randomness Expansion from the Spot-Checking Protocol0 aUniversal Security for Randomness Expansion from the SpotCheckin  c2017/08/010 v463 a<p><span style="font-family: &quot;Lucida Grande&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">Colbeck (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%, 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 (Inventiones mathematicae, 115:463-482, 1994).</span></p>1 aMiller, Carl1 aShi, Yaoyun  uhttp://epubs.siam.org/doi/10.1137/15M1044333