A remarkable representation of the Clifford group

Details A remarkable representation of the Clifford group A remarkable representation of the Clifford group

2012-02-16

arxiv.org/abs/1202.3559v1

Physics

Quantum Physics

6 pages; talk at the Vaxjo conference on Advances in Quantum Theory, 2010

Scientific paper

The finite Heisenberg group knows when the dimension of Hilbert space is a square number. Remarkably, it then admits a representation such that the entire Clifford group --- the automorphism group of the Heisenberg group --- is represented by monomial phase-permutation matrices. This has a beneficial influence on the amount of calculation that must be done to find Symmetric Informationally Complete POVMs. I make some comments on the equations obeyed by the absolute values of the components of the SIC vectors, and on the fact that the representation partly suggests a preferred tensor product structure.

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