Carl A. Miller, University of Michigan, Ann Arbor, USA
Recently Yaoyun Shi and I gave the first proof of security for robust exponential quantum randomness expansion. This talk will be an overview of the problem and a discussion of the techniques used in our proof.
Colbeck's thesis (2006) proposed a scheme whereby quantum devices that are completely untrusted can be used to generate certifiable random numbers. The underlying intuition is simple: if untrusted devices exhibit violations of a Bell inequality, then their outputs must be partially random. Yet, showing that Colbeck's approach is secure has proved to be quite difficult. Our work invents new techniques which prove full security under minimal assumptions. A key idea is the notion that untrusted devices can be used to simulate the behavior of partially-trusted devices. We also introduce a new uncertainty principle for anti-commuting measurements.