We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as: what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e. statistical dependencies which cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states which display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems. Correlations describe global properties which cannot be inferred from the features of the system parts, e.g. phases of many-body systems [5]. They are also resources. Entanglement, a kind of quantum correlation, enables speed-up in quantum information processing [6]. Yet, the very notion of genuine multipartite correlations still generates discussion [7]. There is no consistent way to quantify dependencies which do not manifest bipartite correlations, encoding joint properties of k > 2 particles instead, while witnesses of multipartite entanglement of at least order k have been proposed [8][9][10][11][12][13][14][15]. A further problem is that computing correlations is not always sufficient to fully describe multipartite correlation patterns. Equally correlated networks of multivariate variables can display different structures and properties [16,17]. Also, quantum states can be correlated in inherently inequivalent ways [18][19][20]. Here we propose a framework to describe genuine multipartite correlations in classical and quantum systems. We identify distance-based measures which satisfy a set of desirable properties when parts of the systems are added or discarded, and local operations are performed. We show that adopting the relative entropy allows for simplifying computations and meeting even stronger constraints. We then introduce the notion of weaving to classify multipartite states by studying how correlations scale with their order. The weaving of a state is given by the weighted sum of genuine multipartite correlations of any order, inheriting the properties of correlation measures. We compute the weaving of correlated classical and quantum states. In such cases, states which have equal total correlations or highest order correlations, but display a different correlation pattern, take different weaving values.

We address the problem of optically controlling and quantifying the dissipative dynamics of quantum and classical correlations in a setup of individual quantum emitters under external laser excitation. We show that both types of correlations, the former measured by the quantum discord, are present in the system's evolution even though the emitters may exhibit an early stage disentanglement. In the absence of external laser pumping, we demonstrate analytically, for a set of suitable initial states, that there is an entropy bound for which quantum discord and entanglement of the emitters are always greater than classical correlations, thus disproving an early conjecture that classical correlations are greater than quantum correlations. Furthermore, we show that quantum correlations can also be greater than classical correlations when the system is driven by a laser field. For scenarios where the emitters' quantum correlations are below their classical counterparts, an optimization of the evolution of the quantum correlations can be carried out by appropriately tailoring the amplitude of the laser field and the emitters' dipole-dipole interaction. We stress the importance of using the entanglement of formation, rather than the concurrence, as the entanglement measure, since the latter can grow beyond the total correlations and thus give incorrect results on the actual system's degree of entanglement.

Most works on open quantum systems generally focus on the reduced physical system by tracing out the environment degrees of freedom. Here we show that the qubit distributions with the environment are essential for a thorough analysis, and demonstrate that the way that quantum correlations are distributed in a quantum register is constrained by the way in which each subsystem gets correlated with the environment. For a two-qubit system coupled to a common dissipative environment , we show how to optimise interqubit correlations and entanglement via a quantification of the qubit-environment information flow, in a process that, perhaps surprisingly, does not rely on the knowledge of the state of the environment. To illustrate our findings, we consider an optically-driven bipartite interacting qubit AB system under the action of . By tailoring the light-matter interaction, a relationship between the qubits early stage disentanglement and the qubit-environment entanglement distribution is found. We also show that, under suitable initial conditions, the qubits energy asymmetry allows the identification of physical scenarios whereby qubit-qubit entanglement minima coincide with the extrema of the and entanglement oscillations.

Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players’ input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.