Quantum Correlations Reduce Classical Correlations with Ancillary Systems

We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only if each party of the state can be perfectly correlated with other ancillary systems. In particular, this means that if there are quantum correlations between two parties, then the classical (as well as quantum) correlating capabilities of the two parties with other systems have to be strictly reduced.