Radon-Nikodym derivatives of quantum operations
| dc.creator | Raginsky, Maxim | |
| dc.date | 2003-03-25 | |
| dc.date | 2003-09-16 | |
| dc.date.accessioned | 2026-07-07T04:29:55Z | |
| dc.date.available | 2026-07-07T04:29:55Z | |
| dc.description | Given a completely positive (CP) map $T$, there is a theorem of the Radon-Nikodym type [W.B. Arveson, Acta Math. {\bf 123}, 141 (1969); V.P. Belavkin and P. Staszewski, Rep. Math. Phys. {\bf 24}, 49 (1986)] that completely characterizes all CP maps $S$ such that $T-S$ is also a CP map. This theorem is reviewed, and several alternative formulations are given along the way. We then use the Radon-Nikodym formalism to study the structure of order intervals of quantum operations, as well as a certain one-to-one correspondence between CP maps and positive operators, already fruitfully exploited in many quantum information-theoretic treatments. We also comment on how the Radon-Nikodym theorem can be used to derive norm estimates for differences of CP maps in general, and of quantum operations in particular. | |
| dc.description | 22 pages; final version | |
| dc.identifier | https://arxiv.org/abs/math-ph/0303056 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0303056 | |
| dc.identifier | J. Math. Phys. 44, 5003-5020 (2003) | |
| dc.identifier | doi:10.1063/1.1615697 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57335 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Physics | |
| dc.subject | 46L07, 46L55, 46L60, 47L07 | |
| dc.title | Radon-Nikodym derivatives of quantum operations | |
| dc.type | text |