Note on genuine multipartite classical correlations
  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. 
Andrzej Grudka, Michal Horodecki, Pawel Horodecki, Ryszard Horodecki