"An Interpolation Problem for Completely Positive Maps on Matrices"





Aurelian Gheondea

(Bilkent University)



Abstract: We present certain existence criteria and parametrizations for an interpolation  problem for completely positive maps that take given matrices from a finite set into  prescribed matrices. Our approach uses density matrices associated to linear functionals on $*$-subspaces of matrices, inspired by the Smith-Ward linear  functional and Arveson's Hahn-Banach type Theorem. We perform a careful investigation  on the intricate relation between the positivity of the density matrix and the positivity of the  corresponding linear functional. A necessary and sufficient condition for the existence of  solutions and a parametrisation of the set of all solutions of the interpolation problem in terms  of a closed and convex set of an affine space are obtained. Other linear affine restrictions, like trace preserving, can be included as well, hence covering applications to quantum channels that yield certain quantum states at prescribed quantum states.



Date:  Tuesday, October  1, 2013

Time: 16.00

Place: Mathematics Seminar Room, SA-141



Tea and cookies will be served before the seminar.