  Quantum non-locality is normally defined via violations of Bell's
inequalities that exclude certain classical hidden variable theories from
explaining quantum correlations. Another definition of non-locality refers to
the wave-function collapse thereby one can prepare a quantum state from
arbitrary far away. In both cases one can debate on whether non-locality is a
real physical phenomenon, e.g. one can employ formulations of quantum mechanics
that does not use collapse, or one can simply refrain from explaining quantum
correlations via classical hidden variables. Here we point out that there is a
non-local effect within quantum mechanics, i.e. without involving hidden
variables or collapse. This effect is seen via imprecise (i.e. interval-valued)
joint probability of two observables, which replaces the ill-defined notion of
the precise joint probability for non-commuting observables. It is consistent
with all requirements for the joint probability, e.g. those for commuting
observales. The non-locality amounts to a fact that (in a two-particle system)
the joint imprecise probability of non-commuting two-particle observables (i.e.
tensor product of single-particle observables) does not factorize into
single-particle contributions, even for uncorrelated states of the two-particle
system. The factorization is recovered for a less precise (i.e. the one
involving a wider interval) joint probability. This approach to non-locality
reconciles it with locality, since the latter emerges as a less precise
description.
