Complementarity between signalling and local indeterminacy in quantum nonlocal correlations

Understand

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.