Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.3736
Publisher DOI: 10.3390/e21040435
arXiv ID: 1903.09797v2
Title: Canonical divergence for measuring classical and quantum complexity
Language: English
Authors: Felice, Domenico 
Mancini, Stefano 
Ay, Nihat 
Keywords: Differential geometry; Quantum information; Riemannian geometries; Mathematical Physics; Mathematical Physics; Mathematics - Mathematical Physics; Quantum Physics
Issue Date: 24-Apr-2019
Publisher: MDPI
Source: Entropy 21 (4): 435 (2019-04)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/10195
DOI: 10.15480/882.3736
ISSN: 1099-4300
Journal: Entropy 
Document Type: Article
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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