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2013 Random pure quantum states via unitary Brownian motion
Ion Nechita, Clément Pellegrini
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Electron. Commun. Probab. 18(none): 1-13 (2013). DOI: 10.1214/ECP.v18-2426


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.


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Ion Nechita. Clément Pellegrini. "Random pure quantum states via unitary Brownian motion." Electron. Commun. Probab. 18 1 - 13, 2013.


Accepted: 15 April 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1337.60204
MathSciNet: MR3056064
Digital Object Identifier: 10.1214/ECP.v18-2426

Primary: 39A50
Secondary: 81P45


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