SICs and Algebraic Number Theory |
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| Authors: | Marcus Appleby Steven Flammia Gary McConnell Jon Yard |
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| Institution: | 1.Centre for Engineered Quantum Systems, School of Physics,University of Sydney,Sydney,Australia;2.Center for Theoretical Physics,Massachusetts Institute of Technology,Cambridge,USA;3.Controlled Dynamics Theory Group,Imperial College,London,UK;4.Institute for Quantum Computing, Dept. of Combinatorics and Optimization,University of Waterloo and Perimeter Institute for Theoretical Physics,Waterloo,Canada |
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| Abstract: | We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory. |
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