Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras
Functional Analysis
2023-09-06 v4 Operator Algebras
Quantum Physics
Abstract
We prove a Schoenberg-type correspondence for non-unital semigroups which generalizes an analogous result for unital semigroup proved by Michael Sch\"urmann. It characterizes the generators of semigroups of linear maps on which are -positive, -superpositive, or -entanglement breaking. As a corollary we reprove Lindblad, Gorini, Kossakowski, Sudarshan's theorem. We present some concrete examples of semigroups of operators and study how their positivity properties can improve with time.
Keywords
Cite
@article{arxiv.2301.10679,
title = {Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras},
author = {B. V. Rajarama Bhat and Purbayan Chakraborty and Uwe Franz},
journal= {arXiv preprint arXiv:2301.10679},
year = {2023}
}
Comments
18 pages, v2 contains minor corrections. v3: parts of Section 2 moved to Sections 4 and 6, additional details are inserted in several proofs, and further minor corrections, v4 cibtains final minor corrections