RT Journal Article
T1 A quantum version of Wielandt's inequality
A1 Sanz, Mikel
A1 Pérez García, David
A1 Cirac, Juan I.
A1 Wolf, Michael
AB 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.
PB IEEE
SN 4668-4673
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/41902
UL https://hdl.handle.net/20.500.14352/41902
LA eng
NO Unión Europea. FP7
DS Docta Complutense
RD 11 abr 2025