MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Quantum version of Wielandt's Inequality revisited

Mateusz Michałek and Yaroslav Shitov


Consider a linear space $L$ of complex $D$-dimensional linear operators, and assume that some power $L^k$ of $L$ is the whole space of $D\times D$ matrices. Perez-Garcia, Verstraete, Wolf and Cirac conjectured that the sequence $L^1,L^2,\dots$ stablilizes after $O(D^2)$ terms; we prove that this happens after $O(D^2 \log(D))$ terms, improving the previously known bound of $O(D^4)$.


Related publications

2019 Repository Open Access
Mateusz Michałek and Yaroslav Shitov

Quantum version of Wielandt's inequality revisited

In: IEEE transactions on information theory, 65 (2019) 8, pp. 5239-5242