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Random pure quantum states via unitary Brownian motion

   
@article{ECP2426,
	author = {Ion Nechita and Clément Pellegrini},
	title = {Random pure quantum states via unitary Brownian motion},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {quantum states, unitary Brownian motion},
	abstract = {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.},
	pages = {no. 27, 1-13},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2426},    
        url = {http://ecp.ejpecp.org/article/view/2426}}