Irreducible multiparty correlations can be created by local operations

Abstract

Generalizing Amari's work titled ``Information geometry on hierarchy of probability distributions'' [IEEE Trans. Inf. Theory 47, 1701 (2001)], 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 Neumann entropy principle [Phys. Rev. Lett. 89, 207901 (2002) and Phys. Rev. Lett. 101, 180505 (2008)]. 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, irreducible three-party correlations can be created by local operations from a three-party state with only irreducible two-party correlations. In other words, even if a three-partite state is initially completely determined by measuring two-party Hermitian operators, the determination of the state after local operations has to resort to the measurements of three-party Hermitian operators.