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CATEGORIES:CQIF Seminar
SUMMARY:Irreducible representations of partially transpose
 d permutation operators with applications to quant
 um information problems - Michał Studziński\, Univ
 ersity of Cambridge
DTSTART;TZID=Europe/London:20160128T141500
DTEND;TZID=Europe/London:20160128T151500
UID:TALK63964AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63964
DESCRIPTION:In this talk we show how to construct irreducible 
 representations (irreps) of partially transposed p
 ermutation operators over last subsystem. We give 
 direct method of irreps construction for an arbitr
 ary number of  subsystems n and local Hilbert spac
 e dimension d. Our method is inspired by represent
 ation theory of symmetric group\, especially so ca
 lled Schur-Weyl duality and Walled Brauer Algebras
 . At the end of the talk we consider one possible 
 application of our tool to the problem of universa
 l quantum cloning machines.  Using group- theory f
 ormalism\, we show that the allowed region for fid
 elities (describes quality of the clones) can be e
 xpressed in terms of overlaps of pure states with 
  irreducible representations of the partially  tra
 nsposed  permutation operators.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
 ce Road\, Cambridge
CONTACT:Steve Brierley
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