Fibonacci-Lucas SIC-POVMs

Abstract

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.

arXiv commentThe fiducial vectors can be obtained from http://sicpovm.markus-grassl.de as well as from the source files. v2: precision for the numerical solution in dimension 844 increased to 150 digits and new exact solution for dimension 323 added

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• 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
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• SIC-POVMs from Stark Units: Dimensions n^2+3=4p, p prime
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