A major barrier to understanding open quantum systems is that we lack the tools to bound the mixing times of their associated dynamics. This lack stands in stark contrast to the analogous classical literature, where there is a rich theory of such techniques.
I will describe how to lift the "classic" parts of this classical theory to the quantum world. Quantum Wasserstein distance plays a key role here; upon defining it and developing its properties, it leads us naturally to quantum versions of path-coupling, Dobrushin conditions, and disagreement percolation. This allows us to recover existing results on rapid mixing at high temperature. If time permits, I will touch on our application of this theory to clustering of CMI at high temperature.
Joint work with Ainesh Bakshi, Allen Liu, and Ankur Moitra.
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