  Here, we leverage recent advances in information theory to develop a novel
method to characterise the dominant character of the high-order dependencies of
quantum systems. To this end, we introduce the Q-information: an
information-theoretic measure capable of distinguishing quantum states
dominated by synergy or redundancy. We illustrate the measure by investigating
the properties of paradigmatic entangled Qubit states and find that -- in
contrast to classical systems -- quantum systems need at least four variables
to exhibit high-order properties. Furthermore, our results reveal that unitary
evolution can radically affect the internal information organisation in a way
that strongly depends on the corresponding Hamiltonian. Overall, the
Q-information sheds light on novel aspects of the internal organisation of
quantum systems and their time evolution, opening new avenues for studying
several quantum phenomena and related technologies.
