2017/07/31 by Markus Grassl, Andrew J. Scott · 40 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Conjecture #Dimension (graph theory) #Fibonacci number #Operator (biology) #Statistical Mechanics and Entropy #Symmetry (geometry) #Symmetry group #quant-ph
paper · pdf · doi:10.1063/1.4995444
published in Journal of Mathematical Physics 58(12) (American Institute of Physics) · The 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
openalex created_date 2017/07/21 · arxiv created 2017/09/21 · openalex publication_date 2017/12/01 · arxiv updated 2017/12/05 · openalex updated_date 2026/08/05
We present a conjectured family of symmetric informationally complete positive operator valued measures 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, and 323 as well as a numerical solution for dimension d = 844.