$H_2$-reducible matrices in six-dimensional mutually unbiased bases
Quantum Physics
2021-10-29 v2 Mathematical Physics
math.MP
Abstract
Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the -reducible matrix in the four MUBs has exactly nine Hadamard submatrices. We apply our result to exclude from the four MUBs some known CHMs, such as symmetric -reducible matrix, the Hermitian matrix, Dita family, Bjorck's circulant matrix, and Szollosi family. Our results represent the latest progress on the existence of six-dimensional MUBs.
Keywords
Cite
@article{arxiv.2110.13646,
title = {$H_2$-reducible matrices in six-dimensional mutually unbiased bases},
author = {Xiaoyu Chen and Mengfan Liang and Mengyao Hu and Lin Chen},
journal= {arXiv preprint arXiv:2110.13646},
year = {2021}
}
Comments
15 pages, be published on quantum information processing. arXiv admin note: text overlap with arXiv:1904.10181