Law of Cosines and Shannon-Pythagorean theorem for quantum information

Belavkin, Roman V. (2013) Law of Cosines and Shannon-Pythagorean theorem for quantum information. In: Geometric Science of Information : First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings. Nielsen, Frank and Barbaresco, Frédéric, eds. Lecture Notes in Computer Science, Part X (8085). Springer Verlag, Berlin, pp. 369-376. ISBN 9783642400193

Full text is not in this repository.

Abstract

The concept of information distance in non-commutative setting is re-considered. Additive information, such as Kullback-Leibler divergence, is defined using convex functional with gradient having the property of homomorphism between multiplicative and additive subgroups. We review several geometric properties, such as the logarithmic law of cosines, Pythagorean theorem and a lower bound given by squared Euclidean distance. We also prove a special case of Pythagorean theorem for Shannon information, which finds applications in informationtheoretic variational problems.

Item Type: Book Section
Research Areas: A. > School of Science and Technology > Computer Science
A. > School of Science and Technology > Computer Science > Artificial Intelligence group
Item ID: 13319
Useful Links:
Depositing User: Roman Belavkin
Date Deposited: 23 May 2014 10:09
Last Modified: 13 Oct 2016 14:30
URI: https://eprints.mdx.ac.uk/id/eprint/13319

Actions (login required)

Edit Item Edit Item