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arXiv · 2301.10679

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

B. V. Rajarama Bhat·Purbayan Chakraborty·Uwe Franz
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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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B. V. Rajarama Bhat, Purbayan Chakraborty, Uwe Franz. 2023-01-25. Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras. https://doi.org/10.1007/s11117-023-01003-6

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