Irreducible multiparty correlation can be created by local operations

TL;DR

This paper introduces a quantum information measure for irreducible multiparty correlations, showing that local operations can create such correlations even when total correlations do not increase.

Contribution

It defines irreducible multiparty correlations using quantum relative entropy and proves their equivalence to entropy-based definitions, revealing new properties of local operations.

Findings

Irreducible three-party correlation can be generated by local operations.

Total correlation degree does not increase under local operations.

Determination of the post-operation state requires three-party measurements.

Abstract

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.