Quantifying genuine multipartite correlations and their pattern complexity

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

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.

Citation

Girolami, D., Tufarelli, T., & Susa, C. E. (2017). Quantifying genuine multipartite correlations and their pattern complexity. Physical Review Letters, 119(14), Article 140505. https://doi.org/10.1103/PhysRevLett.119.140505

• 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
• DOI: https://doi.org/10.1103/PhysRevLett.119.140505
• Public URL: https://nottingham-repository.worktribe.com/output/886263
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.140505
• Contract Date: Sep 28, 2017