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Canonical Divergence for Measuring Classical and Quantum Complexity

by 1, 2,3,* and 1,4,5
1
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
2
School of Science and Technology, University of Camerino, I-62032 Camerino, Italy
3
INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
4
Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA
5
Faculty of Mathematics and Computer Science, University of Leipzig, PF 100920, 04009 Leipzig, Germany
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(4), 435; https://doi.org/10.3390/e21040435
Received: 25 March 2019 / Revised: 15 April 2019 / Accepted: 18 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Quantum Entropies and Complexity)
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. View Full-Text
Keywords: riemannian geometries; differential geometry; quantum information riemannian geometries; differential geometry; quantum information
MDPI and ACS Style

Felice, D.; Mancini, S.; Ay, N. Canonical Divergence for Measuring Classical and Quantum Complexity. Entropy 2019, 21, 435.

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