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|Title:||Systems of imprimitivity for the Clifford group|
|Source:||Appleby, D.M.,Bengtsson, I.,Brierley, S.,Ericsson, Å.,Grassl, M.,Larsson, J.-Å. (2014-03-01). Systems of imprimitivity for the Clifford group. Quantum Information and Computation 14 (3-4) : 339-360. ScholarBank@NUS Repository.|
|Abstract:||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). © Rinton Press.|
|Source Title:||Quantum Information and Computation|
|Appears in Collections:||Staff Publications|
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