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.

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