Fibonacci-Lucas SIC-POVMs
Markus Grassl, Andrew J. Scott
TL;DR
This paper proposes a conjectured family of symmetric informationally complete positive operator-valued measures (SIC-POVMs) with symmetries linked to Fibonacci and Lucas numbers, supported by exact and numerical solutions across multiple dimensions.
Contribution
It introduces a new family of SIC-POVMs with Fibonacci-Lucas related symmetries, expanding understanding of symmetric measurement structures in quantum information.
Findings
Exact solutions for dimensions 4, 8, 19, 48, 124, 323.
Numerical solution for dimension 844.
Symmetry group size grows with dimension.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.