A quantum version of Wielandt's inequality
Quantum Physics
2011-06-02 v2 Mathematical Physics
math.MP
Abstract
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero--error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.
Cite
@article{arxiv.0909.5347,
title = {A quantum version of Wielandt's inequality},
author = {M. Sanz and D. Perez-Garcia and M. M. Wolf and J. I. Cirac},
journal= {arXiv preprint arXiv:0909.5347},
year = {2011}
}
Comments
6 pages, no figures