A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total non-classical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by non-classical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite non-classical correlations and is a non-negative quantity, while the latter is related to the monogamy of the non-classical correlations.

Accepted for publication in Physical Review Letters