Random pure quantum states via unitary Brownian motion
نویسندگان
چکیده
We introduce a new family of probability distributions on the set of pure states of a finite dimensional quantum system. Without any a priori assumptions, the most natural measure on the set of pure state is the uniform (or Haar) measure. Our family of measures is indexed by a time parameter t and interpolates between a deterministic measure (t = 0) and the uniform measure (t = ∞). The measures are constructed using a Brownian motion on the unitary group UN . Remarkably, these measures have a UN−1 invariance, whereas the usual uniform measure has a UN invariance. We compute several averages with respect to these measures using as a tool the Laplace transform of the coordinates.
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