The Wiener process (say, on $mathbb{R}$) can be thought of as a scaling limit of a classical, discrete random walk. On the other hand, one can define and study quantum random walks, when the underlying stochastic process is governed by a unitary transform + measurement (for an excellent introduction, see http://arxiv.org/abs/quant-ph/0303081).
My question is - do quantum random walks have a reasonable continuous limit, something which would give a quantum analogue of the Wiener process?
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