  Generalizing Amari's work titled "Information geometry on hierarchy of
probability distributions", we define the degrees of irreducible multiparty
correlations in a multiparty quantum state based on quantum relative entropy.
We prove that these definitions are equivalent to those derived from the
maximal von Neaumann entropy principle. Based on these definitions, we find a
counterintuitive result on irreducible multiparty correlations: although the
degree of the total correlation in a three-party quantum state does not
increase under local operations, the irreducible three-party correlation can be
created by local operations from a three-party state with only irreducible
two-party correlations. In other words, even if a three-party state is
initially completely determined by measuring two-party Hermitian operators, the
determination of the state after local operations have to resort to the
measurements of three-party Hermitian operators.
