Order-Six CHMs Containing Exactly Three Distinct Elements
Abstract
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 kinds of matrices, one is H 2 -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 ℂ 6 consists of an MUB trio and the identity) since we find that neither of the two CHMs belong to any MUB trio. Our results may lead to the more complete classification of 6 × 6 CHMs whose elements in the first row are all 1.
Fields of Study & Subjects
Inorganic Chemistry and Materials
Machine Learning in Materials Science
Synthesis and characterization of novel inorganic/organometallic compounds
Publication details
- Journal / source
- Quantum Information and Computation
- Publisher
- Walter de Gruyter GmbH
- Volume
- 26
- Issue
- 1
- Pages
- 1–19
- Publication date
- 1 March 2026
- Language
- EN