If intrinsic randomness is the answer, what's the question?
S. Aravinda, R. Srikanth · arXiv (Cornell University) · 2013
The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell’s theorem, and can be used to certify randomness in a device-independent way, assuming neither the validity of quantum mechanics nor even no-signaling. We obtain general nonlocal resources that can simulate the statistics of the singlet state, encompassing existing results. We prove a conjecture due to Hall (2010) and Kar et al. (2011) on the complementarity for such resources. Further, we show that signaling leads to biasing of the marginals for these resources. This entails that no-signaling is a consequence of isotropic unbiasedness of the singlet statistics, by which is meant that the marginals are unbiased along any direction, and coincidence counts are determined only by the relative orientation of pairs of polarizers.