There are currently PhD openings (including in quantum information theory) in the Department of Mathematical Sciences, University of Copenhagen. For more information see:
http://www.math.ku.dk/english/about/jobs/phd-stipends-fall-2014/
Please note that the deadline is very soon (10th of May 2014).
Best wishes, Matthias.
Matthias Christandl
Professor
Department of Mathematical Sciences
Copenhagen University
email: christandl [at] math [dot] ku [dot] dk