An Effective Way of Characterizing the Quantum Nonlocality

Nonlocality is a distinctive feature of quantum theory, which has been extensively studied for decades. It is found that the uncertainty principle determines the nonlocality of quantum mechanics. Here we show that various degrees of nonlocalities in correlated system can be characterized by the generalized uncertainty principle, by which the complementarity is attributed to the mutual dependence of observables. Concrete examples for different kinds of non-classical phenomena pertaining to different orders of dependence are presented. We obtain the third order ``skewness nonlocality'', and find that the Bell nonlocality turns out to be merely the second order ``variance nonlocality'' and the forth order dependence contains the commutator squares, which hence is related to the quantum contextuality. More applications of the generalized uncertainty principle are expected.