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Systems of Imprimit...
Systems of Imprimitivity for the Clifford Group
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- Appleby, D.M. (författare)
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
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- Bengtsson, Ingemar (författare)
- Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden
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- Brierley, Stephen (författare)
- Heilbronn Institute for Mathematical Research, Department of Mathematics, University of Bristol, United Kingdom
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- Ericsson, Åsa (författare)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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- Grassl, Markus (författare)
- Centre for Quantum Technologies, National University of Singapore, Singapore
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- Larsson, Jan-Åke (författare)
- Linköpings universitet,Informationskodning,Tekniska högskolan
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(creator_code:org_t)
- Rinton Press, 2014
- 2014
- Engelska.
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Ingår i: Quantum information & computation. - : Rinton Press. - 1533-7146. ; 14:3-4, s. 339-360
- Relaterad länk:
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http://dl.acm.org/ci...
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.2...
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Abstract
Ämnesord
Stäng
- 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).
Nyckelord
- Clifford group
- SIC POVM
- Sparse representation
- TECHNOLOGY
- TEKNIKVETENSKAP
Publikations- och innehållstyp
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- art (ämneskategori)
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