Systems of Imprimitivity for the Clifford Group

Appleby, D.M.Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada (författare)

It is known that if the dimension is a perfect square the Clifford group can be represented by monomial matrices. Another way of expressing this result is to say that when the dimension is a perfect square the standard representation of the Clifford group has a system of imprimitivity consisting of one dimensional subspaces. We generalize this result to the case of an arbitrary dimension. Let k be the square-free part of the dimension. Then we show that the standard representation of the Clifford group has a system of imprimitivity consisting of k-dimensional subspaces. To illustrate the use of this result we apply it to the calculation of SIC-POVMs (symmetric informationally complete positive operator valued measures), constructing exact solutions in dimensions 8 (hand-calculation) as well as 12 and 28 (machine-calculation).

Bengtsson, IngemarStockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden (författare)
Brierley, StephenHeilbronn Institute for Mathematical Research, Department of Mathematics, University of Bristol, United Kingdom (författare)
Ericsson, ÅsaLinköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan(Swepub:liu)asaer02 (författare)
Grassl, MarkusCentre for Quantum Technologies, National University of Singapore, Singapore (författare)
Larsson, Jan-ÅkeLinköpings universitet,Informationskodning,Tekniska högskolan(Swepub:liu)janla64 (författare)
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, CanadaStockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden (creator_code:org_t)

Ingår i:Quantum information & computation: Rinton Press14:3-4, s. 339-3601533-7146

Av författaren/redakt...: Appleby, D.M.; Bengtsson, Ingem ...; Brierley, Stephe ...; Ericsson, Åsa; Grassl, Markus; Larsson, Jan-Åke

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.