Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416353 | Linear Algebra and its Applications | 2015 | 11 Pages |
Abstract
The complete classification of all 6Ã6 complex Hadamard matrices is an open problem. The 3-parameter Karlsson family encapsulates all Hadamards that have been parametrised explicitly. We prove that such matrices satisfy a non-trivial constraint conjectured to hold for (almost) all 6Ã6 Hadamard matrices. Our result imposes additional conditions in the linear programming approach to the mutually unbiased bases problem recently proposed by Matolcsi et al. Unfortunately running the linear programs we were unable to conclude that a complete set of mutually unbiased bases cannot be constructed from Karlsson Hadamards alone.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrew S. Maxwell, Stephen Brierley,