Order-six CHMs containing exactly three distinct elements
Abstract
Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the least number of distinct elements. In this paper, we show that such CHMs can only be complex equivalent to two kind of matrices, one is H2-reducible and the other is the Tao matrix. Using our result one can further narrow the range of MUB trio (a set of four MUBs in C6 consists of an MUB trio and the identity) since we find that the two CHMs neither belong to MUB trios. Our results may lead to the more complete classification of 6× 6 CHMs whose elements in the first row are all 1.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.