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Quantifying Genuine Multipartite Correlations and their Pattern Complexity.

Davide Girolami1, Tommaso Tufarelli2, Cristian E Susa3

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Summary
This summary is machine-generated.

We developed a new framework to measure multipartite correlations in classical and quantum systems. This approach quantifies complex statistical dependencies and classifies states based on their correlation patterns.

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Area of Science:

  • Physics
  • Information Theory
  • Complexity Science

Background:

  • Quantifying multipartite correlations is crucial for understanding complex classical and quantum systems.
  • Existing measures often struggle to capture genuine multipartite dependencies distinct from bipartite correlations.

Purpose of the Study:

  • To propose an information-theoretic framework for quantifying multipartite correlations.
  • To identify measures of genuine multipartite correlations with desirable properties.
  • To introduce a new concept, 'weaving,' for classifying states based on correlation patterns.

Main Methods:

  • Development of an information-theoretic framework.
  • Identification of measures for genuine multipartite correlations.
  • Introduction of the 'weaving' concept, defined as a weighted sum of correlations of all orders.

Main Results:

  • The framework successfully quantifies multipartite correlations, addressing questions like the amount of seven-partite correlations in a ten-particle system.
  • New measures for genuine multipartite correlations were identified, satisfying key properties.
  • The 'weaving' concept provides a method to classify states with similar correlation measures but different underlying structures.

Conclusions:

  • The proposed information-theoretic framework offers a robust way to quantify multipartite correlations.
  • Genuine multipartite correlation measures and the weaving concept enhance our understanding of complex systems.
  • Weaving measures effectively describe the complexity of correlation structures in multipartite systems.