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Quantifying genuine multipartite correlations and their pattern complexity

Girolami, Davide; Tufarelli, Tommaso; Susa, Cristian E.


Davide Girolami

Cristian E. Susa


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.


Girolami, D., Tufarelli, T., & Susa, C. E. (2017). Quantifying genuine multipartite correlations and their pattern complexity. Physical Review Letters, 119(14), Article 140505.

Journal Article Type Article
Acceptance Date Sep 12, 2017
Publication Date Oct 5, 2017
Deposit Date Sep 28, 2017
Publicly Available Date Oct 5, 2017
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 119
Issue 14
Article Number 140505
Public URL
Publisher URL


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