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SUMMARY:Irreducible representations of partially transposed permutation op
 erators with applications to quantum information problems - Michał Studzi
 ński\, University of Cambridge
DTSTART:20160128T141500Z
DTEND:20160128T151500Z
UID:TALK63964@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:In this talk we show how to construct irreducible representati
 ons (irreps) of partially transposed permutation operators over last subsy
 stem. We give direct method of irreps construction for an arbitrary number
  of  subsystems n and local Hilbert space dimension d. Our method is inspi
 red by representation theory of symmetric group\, especially so called Sch
 ur-Weyl duality and Walled Brauer Algebras. At the end of the talk we cons
 ider one possible application of our tool to the problem of universal quan
 tum cloning machines.  Using group- theory formalism\, we show that the al
 lowed region for fidelities (describes quality of the clones) can be expre
 ssed in terms of overlaps of pure states with  irreducible representations
  of the partially  transposed  permutation operators.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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