%0 Journal Article
%A Sanz, Mikel
%A Pérez García, David
%A Cirac, Juan I.
%A Wolf, Michael
%T A quantum version of Wielandt's inequality
%D 2010
%@ 4668-4673
%U https://hdl.handle.net/20.500.14352/41902
%X 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.
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