Quantum Randomness Expansion - New Results
Carl Miller, University of Michigan
Is it possible to create a source of provable random numbers? An affirmative answer to this question would be highly useful in information security, where random numbers are needed to provide the keys for encryption algorithms. Bell inequality violation experiments offer hope for this problem, since the outputs of a Bell violation must be non-classical and therefore not fully predictable to an adversary. The challenge is to prove something stronger: that the outputs can be processed (extracted) to obtain uniformly random data. This leads to some complex and beautiful mathematics.In this talk I will present my work with Yaoyun Shi, which gave the first error-tolerant proof of random number generation from Bell violations. Our most recent paper shows that any violation of the Clauser-Horne-Shimony-Holt inequality (among others) can be used to produce uniform randomness. I will highlight some of the tools we used in the proof, including an old result on the geometry of the Schatten norm.