Quantifying high-order interdependencies in entangled quantum states

We leverage recent advances in information theory to develop a method to characterize 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 organization in a way that strongly depends on the corresponding Hamiltonian. Overall, the Q-information sheds light on aspects of the internal organization of quantum systems and their time evolution, opening different avenues for studying several quantum phenomena and related technologies.