Is it possible to create a source of provable random numbers?  If the answer to this question is "yes," it would be of importance in information security, where the safety of protocols such as RSA depends on the ability to generate random encryption keys.  Bell inequality violations offer a potential solution: if a device exhibits a Bell inequality violation, then its outputs must have been computed by some quantum process and are therefore random.  But, quantifying the amount of randomness that arises by this method is a difficult problem, and it motivates some intricate and beautiful mathematics.

In the talk I will present my work with Yaoyun Shi, which offered the first robust security proof for randomness expansion from Bell inequality violations.  Any violation of the Clauser-Horne-Shimony-Holt inequality (as well as others) can be used to produce uniformly random bits.  Our proofs, though they involve some mathematical heavy-lifting, ultimately reduce to two simple principles.   The first is the notion of self-testing: for some Bell inequalities, a maximal violation allows us to deduce both the state and the measurements used.  The second is a principle of measurement disturbance: if a measurement significantly alters a quantum state, then the outcome of the measurement must be random.

References: arXiv:1411.6608 and arXiv:1402.0489.