Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras

• URL: http://arxiv.org/abs/2301.10679v4
• Date: Fri, 28 Jul 2023 18:05:12 GMT
• Title: Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras
• Authors: B. V. Rajarama Bhat and Purbayan Chakraborty and Uwe Franz
• Abstract summary: It characterizes the generators of semigroups of linear maps on $M_n(C)$ which are $k$-positive, $k$-superpositive, or $k$-entanglement breaking. We present some concrete examples of semigroups of operators and study how their positivity properties can improve with time.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $M_n(C)$ which are $k$-positive, $k$-superpositive, or $k$-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.

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