We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.
@article{arxiv.0802.1633,
title = {Note on genuine multipartite classical correlations},
author = {Andrzej Grudka and Michal Horodecki and Pawel Horodecki and Ryszard Horodecki},
journal= {arXiv preprint arXiv:0802.1633},
year = {2008}
}