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Article Dans Une Revue Positivity Année : 2023

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

Résumé

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 $M_n(\mathbb{C})$ 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 semigroup of operators and study how their positivity properties can improve with time.

Dates et versions

hal-03959683 , version 1 (27-01-2023)

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B. V. Rajarama Bhat, Purbayan Chakraborty, Uwe Franz. Schoenberg Correspondence for $k$-(super)Positive Maps on Matrix Algebras. Positivity, 2023, 27 (4), pp.51. ⟨10.1007/s11117-023-01003-6⟩. ⟨hal-03959683⟩
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