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Characterizing the complete hierarchy of correlations in an $n$-party system

D. L. Zhou·L. You
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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 ($2\le k\le n$). 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.

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D. L. Zhou, L. You. 2007-01-07. Characterizing the complete hierarchy of correlations in an $n$-party system. https://arxiv.org/abs/quant-ph/0701029

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