Role of measurement incompatibility and uncertainty in determining nonlocality (Q515448)

Summary: It has been recently shown that measurement incompatibility and fine grained uncertainty -- a particular form of preparation uncertainty relation -- are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of \textit{R. W. Spekkens} [``Evidence for the epistemic view of quantum states: a toy theory'', Phys. Rev. A75, No. 3, Article ID 032110, 30 p. (2007; \url{doi:10.1103/PhysRevA.75.032110})] shows no nonlocal feature even though steering is present in this theory.