  Bell's theorem is a no-go theorem stating that quantum mechanics cannot be
reproduced by a physical theory based on realism, freedom to choose
experimental settings and two locality conditions: setting (SI) and outcome
(OI) independence. We provide a novel analysis of what it takes to violate
Bell's inequality within the framework in which both realism and freedom of
choice are assumed, by showing that it is impossible to model a violation
without having information in one laboratory about both the setting and the
outcome at the distant one. While it is possible that outcome information can
be revealed from shared hidden variables, the assumed experimenter's freedom to
choose the settings forces that setting information must be non-locally
transferred, even when the SI condition is obeyed. The sufficient amount of
transmitted information about the setting to violate the CHSH inequality up to
its quantum mechanical maximum is 0.736 bits.
