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arXiv · 1402.2448

Diagonal Couplings of Quantum Markov Chains

Burkhard Kümmerer·Kay Schwieger
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Abstract

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.

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Burkhard Kümmerer, Kay Schwieger. 2014-02-11. Diagonal Couplings of Quantum Markov Chains. https://arxiv.org/abs/1402.2448

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