Quantum channels that preserve entanglement
| dc.creator | Arveson, William | |
| dc.date | 2008-01-16 | |
| dc.date | 2008-01-17 | |
| dc.date.accessioned | 2026-07-07T08:54:52Z | |
| dc.date.available | 2026-07-07T08:54:52Z | |
| dc.description | Let M and N be full matrix algebras. A unital completely positive (UCP) map ϕ:M\to N is said to preserve entanglement if its inflation ϕ\otimes \id_N : M\otimes N\to N\otimes N has the following property: for every maximally entangled pure state ρof N\otimes N, ρ\circ(ϕ\otimes \id_N) is an entangled state of M\otimes N. We show that there is a dichotomy in that every UCP map that is not entanglement breaking in the sense of Horodecki-Shor-Ruskai must preserve entanglement, and that entanglement preserving maps of every possible rank exist in abundance. We also show that with probability 1, {\em all} UCP maps of relatively small rank preserve entanglement, but that this is not so for UCP maps of maximum rank. | |
| dc.description | 14 pages, links to references are now fixed | |
| dc.identifier | https://arxiv.org/abs/0801.2531 | |
| dc.identifier | http://arxiv.org/abs/0801.2531 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146097 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | Quantum Physics | |
| dc.subject | 46N50,81P68, 94B27 | |
| dc.title | Quantum channels that preserve entanglement | |
| dc.type | text |