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Random pure quantum states via unitary Brownian motion


 
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1. Title Title of document Random pure quantum states via unitary Brownian motion
 
2. Creator Author's name, affiliation, country Ion Nechita; CNRS, Université de Toulouse; France
 
2. Creator Author's name, affiliation, country Clément Pellegrini; Université de Toulouse; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) quantum states, unitary Brownian motion
 
3. Subject Subject classification 39A50; 81P45
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR/CNRS
 
7. Date (YYYY-MM-DD) 2013-04-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2426
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2426
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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