Quantifying genuine multipartite correlations and their pattern complexity

Abstract

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.

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References in corpus (31)

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• Three qubits can be entangled in two inequivalent ways
• Entanglement detection
• Unified View of Quantum and Classical Correlations
• Four qubits can be entangled in nine different ways
• Classification of mixed three-qubit states
• Quantum tensor product structures are observable-induced
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• Irreducible multi-particle correlations in states without maximal rank
• Hierarchies of multi-partite entanglement
• Witnessing multipartite entanglement by detecting asymmetry
• Geometric phase of an atom in a magnetic storage ring
• Optimal witnessing of the quantum Fisher information with few measurements
• Complexity Measures from Interaction Structures
• Genuine Multipartite Entanglement without Multipartite Correlations
• Computing complexity measures for quantum states based on exponential families
• Overcoming ambiguities in classical and quantum correlation measures
• Irreducible multiparty correlation can be created by local operations
• Quantifying structure in networks
• Complexity measures, emergence, and multiparticle correlations

Cited by in corpus (26)

• Genuine quantum correlations in quantum many-body systems: a review of recent progress
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• Genuine Multipartite Correlations in a Boundary Time Crystal
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Redundantly amplified information suppresses quantum correlations in many-body systems
• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• How much entanglement can be created in a closed system?
• Coherence and quantum correlations measure sensitivity to dephasing channels
• A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information
• Hierarchy of Genuine Multipartite Quantum Correlations
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model
• Correlations break homogenization
• Random unitaries, Robustness, and Complexity of Entanglement
• Higher dimensional entanglement without correlations
• Genuine multipartite correlations in Dicke Superradiance
• Quantifying Information Extraction using Generalized Quantum Measurements
• Experimental demonstration of spontaneous symmetry breaking with emergent multi-qubit entanglement
• Weaving and neural complexity in symmetric quantum states
• Genuine $k$-partite correlations and entanglement in the ground state of the Dicke model for interacting qubits
• Exploring entanglement in finite-size quantum systems with degenerate ground state
• Quantitative bounds to propagation of quantum correlations in many-body systems
• Emergence of global receptive fields capturing multipartite quantum correlations
• Dynamics of tripartite correlations for three qubits in independent thermal reservoirs
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems
• Cooperation and dependencies in multipartite systems