Abstract

A characterization of the complete correlation structure in an n-party system is proposed in terms of a series of (k, n) threshold classical secret sharing protocols (2 ≤ k ≤ n). The total correlation is shown to be the sum of independent correlations of 2-, 3-,…, n-parties. Our result unifies several earlier scattered works, and shines new light at the important topic of multi-party quantum entanglement. As an application, we explicitly construct the hierarchy of correlations in an n-qubit graph state.

© 2008 Optical Society of America