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It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes to appearing is in ...

The cardinality of a finite set $X$ is the number of its elements. Once you know that, you would define the groupoid cardinality of a $\infty$-groupoid $X$ as the quantity $$\lvert X\rvert := \sum_{[x]...

The quantum set-up has many settings, so let's fix some definitions. I will be taking the Hilbert space approach with a minor modification that I will make explicit. We begin with a Hilbert space $\...