Maximizing the divergence from a hierarchical model of quantum states

Abstract

We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.

18 pages, 1 figure, v2: improved exposition, v3: less typos

References in corpus (6)

• On the quantum, classical and total amount of correlations in a quantum state
• On the toric algebra of graphical models
• Using Separable Bell-Diagonal States to Distribute Entanglement
• Computing complexity measures for quantum states based on exponential families
• Complexity classification of local Hamiltonian problems
• The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics

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• A new signature of quantum phase transitions from the numerical range
• A variation principle for ground spaces
• Quantum marginals, faces, and coatoms
• Separability criteria based on the Weyl operators
• Canonical divergence for flat $\alpha$-connections: Classical and Quantum
• An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information