2014/02/11 by Kümmerer, Burkhard, Schwieger, Kay
#46L55 (37A55 #47A35 #81U99) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1402.2448
In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that on a dense subset the coupling is a dual version of the extended dual transition operator previously studied by Gohm etal. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.