Titel: Perturbation Theory for Fixed Points of Quantum Channels
Abstract: It is clear that if the transition matrix of an irreducible
quantum Markov-process has a sub dominant eigenvalue which is close to
1 then the quantum Markov-process is ill conditioned in the sense that
there are stationary states which are sensitive to perturbations in
the transition matrix. However, the converse of this statement has
heretofore been unresolved. The purpose of this talk is to present
upper and lower bounds on the condition number of the chain such that
the bounding terms are determined by the closeness of the sub dominant
eigenvalue to unity.
We obtain perturbation bounds which relate the sensitivity of the
chain under perturbation to its rate of convergence to stationarity.