Sanz, MikelPérez García, DavidCirac, Juan I.Wolf, Michael2023-06-202023-06-2020104668-467310.1109/TIT.2010.2054552https://hdl.handle.net/20.500.14352/41902In 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.engjournal articlehttp://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5550282open access51-73530.145Teoría cuánticaFísica matemáticaQuantum PhysicsMathematical PhysicsTerms—classical channelsInformation ratesQuantum channelsSpin systemsStrongly correlated electronsWielandt’s inequalityFísica matemáticaTeoría de los quanta2210.23 Teoría Cuántica