Roots of Completely Positive Maps
| Autor: | Robin Hillier, U. Vijaya Kumar, B. V. Rajarama Bhat, Nirupama Mallick |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Pure mathematics Quantum Physics Algebra and Number Theory 010102 general mathematics Probability (math.PR) Mathematics - Operator Algebras FOS: Physical sciences 010103 numerical & computational mathematics Divisibility rule 01 natural sciences Embedding problem Operator algebra FOS: Mathematics Discrete Mathematics and Combinatorics 46L57 81P45 Geometry and Topology 0101 mathematics Operator Algebras (math.OA) Quantum Physics (quant-ph) Quantum Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1812.08123 |
| Popis: | We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We present structural and general existence and non-existence results, some special examples in settings where we understand the situation better, and several challenging open problems. Our study is closely related to Elfving's embedding problem in classical probability and the divisibility problem of quantum channels. Comment: 16 pages, v2: minor corrections, added references, to appear in Lin. Alg. Appl |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|