Ion Nechita, Clément Pellegrini
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 ($t=\infty$). The measures are constructed using a Brownian motion on
the unitary group $\mathcal U_N$. Remarkably, these measures have a $\mathcal
U_{N-1}$ invariance, whereas the usual uniform measure has a $\mathcal U_N$
invariance. We compute several averages with respect to these measures using as
a tool the Laplace transform of the coordinates.
View original:
http://arxiv.org/abs/1201.5333
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