2012/02/16 by Ingemar Bengtsson, Bengtsson, Ingemar
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Physical sciences #Finite Group Theory Research #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1202.3559
openalex publication_date 2012/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.