The Effects of Free Will on Randomness Expansion

Abstract

One of the assumptions of Bell’s Theorem is the existence of experimental free will, meaning that measurement settings can be chosen perfectly at random. With the advent of quantum information, the violation of a Bell inequality constitutes evidence of the lack of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. Relaxing the free will assumption changes the bounds on an eavesdropper. We consider a no-signalling model with reduced free will and bound the eavesdropper’s capabilities in the randomness expansion setting. We compare the case where the only allowable probability distributions are ones that are factorizable with the case where any general probability distribution is allowed, explicitly giving optimal no-signalling models for maximal violation.