A quantum version of Wielandt's inequality

Details A quantum version of Wielandt's inequality A quantum version of Wielandt's inequality

2009-09-29

arxiv.org/abs/0909.5347v2

IEEE Trans. Inf. Theory 56 (2010) 4668-4673

Physics

Quantum Physics

6 pages, no figures

Scientific paper

10.1109/TIT.2010.2054552

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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