Mutual Correlation

2025/06/09 by Francesco A. Evangelista, Evangelista, Francesco A. · 1 citation
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2506.07344

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. Benchmark studies on model systems, including H₁₀, N₂, and p-benzyne, demonstrate its efficacy and computational advantage compared to entropy-based metrics such as orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states.

Citations

• Are Molecules Magical? Non-Stabilizerness in Molecular Bonding
• How many distinct and reliable multireference diagnostics are there?
• Forte: A Suite of Advanced Multireference Quantum Chemistry Methods
• Natural orbitals and sparsity of quantum mutual information
• Exploring Hilbert space on a budget: Novel benchmark set and performance\n metric for testing electronic structure methods in the regime of strong\n correlation
• The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
• A diagnostic for determining the quality of single-reference electron correlation methods
• Distributed Entanglement
• Quantifying Entanglement
• Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction

Cited by

• Toward an affordable density-based measure for the quality of a coupled cluster calculation

Related

• Maximal mutual correlation: an algebraic measure of correlations in bipartite quantum systems
• Natural orbitals and sparsity of quantum mutual information
• On correlations and mutual entropy in quantum composed systems
• Tensor product expansions for correlation in quantum many-body systems
• Measuring multipartite quantum correlations by thermodynamic work extraction