Canonical divergence for measuring classical and quantum complexity

Publikationstyp
Journal Article
Date Issued
2019-04-24
Sprache
English
Author(s)
Felice, Domenico  
Mancini, Stefano  
Ay, Nihat  
TORE-DOI
10.15480/882.3736
TORE-URI
http://hdl.handle.net/11420/10195
Journal
Entropy  
Volume
21
Issue
4
Article Number
435
Citation
Entropy 21 (4): 435 (2019-04)
Publisher DOI
10.3390/e21040435
Scopus ID
2-s2.0-85065582634
ArXiv ID
1903.09797v2
Publisher
MDPI
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.
Subjects
Differential geometry
Quantum information
Riemannian geometries
Mathematical Physics
Mathematical Physics
Mathematics - Mathematical Physics
Quantum Physics
DDC Class
004: Informatik
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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