Diagonal couplings of quantum Markov chains
B Kümmerer, K Schwieger - Infinite Dimensional Analysis, Quantum …, 2016 - World Scientific
B Kümmerer, K Schwieger
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2016•World ScientificIn this paper 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 the
coupling is a dual version of the extended dual transition operator studied by Gohm et al. We
deduce that this coupling is successful if and only if the dilation is asymptotically complete.
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 the
coupling is a dual version of the extended dual transition operator studied by Gohm et al. We
deduce that this coupling is successful if and only if the dilation is asymptotically complete.
In this paper 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 the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.
World Scientific