# Quantum mutual information and quantumness vectors for multi-qubit systems. (arXiv:1607.05155v2 [quant-ph] UPDATED)

We introduce a new information theoretic measure of quantum correlations for

multiparticle systems. We use a form of multivariate mutual information -- the

interaction information and generalize it to multiparticle quantum systems.

There are a number of different possible generalizations. We consider two of

them. One of them is related to the notion of quantum discord and the other to

the concept of quantum dissension. This new measure, called dissension vector,

is a set of numbers -- quantumness vector. This can be thought of as a

fine-grained measure, as opposed to measures that quantify some average quantum

properties of a system. These quantities quantify/characterize the correlations

present in multiparticle states. We consider some multiqubit states and find

that these quantities are responsive to different aspects of quantumness, and

correlations present in a state. We find that different dissension vectors can

track the correlations (both classical and quantum), or quantumness only. As

physical applications, we find that these vectors might be useful in several

information processing tasks. We consider the role of dissension vectors -- (a)

in deciding the security of BB84 protocol against an eavesdropper and (b) in

determining the possible role of correlations in the performance of Grover

search algorithm. Especially, in the Grover search algorithm, we find that

dissension vectors can detect the correlations and show the maximum

correlations when one expects.