Law of cosines and Shannon-Pythagorean theorem for quantum information
Book chapter
Belavkin, R. 2013. Law of cosines and Shannon-Pythagorean theorem for quantum information. in: Nielsen, F. and Barbaresco, F. (ed.) Geometric Science of Information : First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings Berlin Springer.
| Chapter title | Law of cosines and Shannon-Pythagorean theorem for quantum information |
|---|---|
| Authors | Belavkin, R. |
| 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. |
| Research Group | Artificial Intelligence group |
| Book title | Geometric Science of Information : First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings |
| Editors | Nielsen, F. and Barbaresco, F. |
| Publisher | Springer |
| Event | 1st International Conference on Geometric Science of Information |
| Place of publication | Berlin |
| Series | Lecture Notes in Computer Science |
| ISBN | |
| Paperback | 9783642400193 |
| Electronic | 9783642400209 |
| ISSN | 0302-9743 |
| Electronic | 1611-3349 |
| Publication dates | |
| Online | 19 Aug 2013 |
| 08 Aug 2013 | |
| Publication process dates | |
| Deposited | 23 May 2014 |
| Output status | Published |
| Digital Object Identifier (DOI) | https://doi.org/10.1007/978-3-642-40020-9_40 |
| Scopus EID | 2-s2.0-84884963577 |
| Related Output | |
| Has metadata | http://www.scopus.com/inward/record.url?eid=2-s2.0-84884963577&partnerID=MN8TOARS |
| Language | English |
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