### Operator norm convergence for sequence of matrices and application to QIT

Collins, B *(University of Ottawa and AIMR)*

Tuesday 15 October 2013, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

Random matrix theory is the study of probabilistic quantities associated to random matrix models, in the large dimension limit. The eigenvalues counting measure and the eigenvalues spacing are amongst the most studied and best understood quantities. The purpose of this talk is to focus on a quantity that was less understood until recently, namely the operator norm of random matrices. I will state recent results in this direction, and mention three applications to quantum information theory: -a- convergence of the collection of images of pure states under typical quantum channels (joint with Fukuda and Nechita) -b- thresholds for random states to have the absolute PPT property (joint with Nechita and Ye), -c- new examples of k-positive maps (ongoing, joint with Hayden and Nechita).

#### Presentation

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