Quantifying High-Order Interdependencies in Entangled Quantum States

TL;DR

This paper introduces Q-information, an information-theoretic measure to analyze high-order dependencies in quantum states, revealing unique properties of quantum systems and their evolution.

Contribution

The paper presents a new measure, Q-information, to characterize high-order interdependencies in quantum states, highlighting differences from classical systems and effects of unitary evolution.

Findings

Quantum systems require at least four variables for high-order properties.

Unitary evolution significantly alters internal information organization.

Q-information provides new insights into quantum system organization and dynamics.

Abstract

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.