# 7 mars 2023: 1 événement

### Mardi 7 mars 13:45-15:00 - Purbayan Chakraborty - LMB

Error basis and characterisation of semigroups of positive maps

Résumé : An unitary error basis on $M_n$ is a generalisation of Pauli matrices which form an orthonormal basis of $M_2$ with respect to Hilbert-Schmidt inner product. Taking advantage of the isomorphism between $M_n\otimes M_n$, $L(M_n)$ the space of linear maps from $M_n$ to itself and $M_n^2$, these unitary error bases are very useful to get a suitable discrete Fourier expansion of a map $T\in L(M_n)$ . These discrete Fourier coefficients which can be thought of as an $n^2\times n^2$ matrix, give many information about different positivity property of the map $T$.
We will discuss a generalised version of Schoenberg correspondence for positive semigroup leading to the characterisation of k-(super)positive operators. As an explicit application we will apply our result for the characterisation of all positive semigroup of linear maps on $M_2$ using Pauli basis.

Lieu : Salle 316 B bis (3ème étage) - Laboratoire de Mathématiques de Besançon (LmB)
Campus de la Bouloie, bâtiment Métrologie B
Université de Franche-Comté
16 route de Gray
25030 Besançon

En savoir plus : Séminaire d’Analyse Fonctionnelle