Systems of Imprimitivity for the Clifford Group
| Autor: | Appleby, D. M., Bengtsson, Ingemar, Brierley, Stephen, Ericsson, Åsa, Grassl, Markus, Larsson, Jan-Åke |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Quantum Information and Computation, Vol. 14, No. 3 & 4, 0339-0360 (2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.26421/QIC14.3-4-9 |
| Popis: | 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). Comment: 28 pages, AMS latex |
| Databáze: | arXiv |
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