  Quantum correlations that violate the Bell inequality cannot be explained by
any (measurement independent) local hidden variable theory. However, the
violation only implies incompatibility of the underlying assumptions of
reality, locality, and measurement independence, and does not address the
extent to which each assumption is violated quantitatively. In contrast, Hall
(2010,2011) gave a quantification of each assumption and generalized the
Bell-CHSH inequality that gives a trade-off relationship between the underlying
assumptions. In this paper, we introduce a quantification of hidden variables
(hiddenness) and derive a new trade-off relation between the hiddenness and the
measurement dependency that holds for any local hidden variable theory.

Quantum Physics