Quantum mutual information and quantumness vectors for multi-qubit systems

Characterization of the correlations of a multiparticle system remains an open problem. We generalize the notion of quantum discord, using multivariate mutual information, to characterize the quantum properties of a multiparticle system. This new measure, called dissension, is a set of numbers – quantumness vector. There are a number of different possible generalizations. We consider two of them. The Track-I generalization is discord type, while the Track-II generalization is based on all possible measurements. We give expressions for these generalizations for n-qubit systems, and explore some of their properties. We also consider a set of three-qubit and four-qubit states to illustrate the usefulness of the dissension vector.