Canonical divergence for measuring classical and quantum complexity

Abstract

A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with the Kullback-Leibler divergence, which is used to quantify how much a probability measure deviates from the non-interacting states that are modeled by exponential families of probabilities. On the space of positive density operators, we prove that the same divergence reduces to the quantum relative entropy, which quantifies many-party correlations of a quantum state from a Gibbs family.

17 pages

References in corpus (5)

• Quantifying Entanglement
• Information geometric methods for complexity
• Hamilton-Jacobi approach to Potential Functions in Information Geometry
• Computing complexity measures for quantum states based on exponential families
• Maximizing the divergence from a hierarchical model of quantum states

Cited by in corpus (7)

• From the Jordan product to Riemannian geometries on classical and quantum states
• Quantum States, Groups and Monotone Metric Tensors
• Parameter-free description of the manifold of non-degenerate density matrices
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions
• G-dual teleparallel connections in Information Geometry
• Group actions and monotone metric tensors: The qubit case
• Canonical divergence for flat $\alpha$-connections: Classical and Quantum