Triplets of Mutually Unbiased Bases
Combinatorics
2025-07-22 v2
Abstract
We initiate a systematic study of triplets of mutually unbiased bases (MUBs). We show that in each MUB-triplet is characterized by a object that we call a Hadamard cube. We describe the basic properties of Hadamard cubes, and show how an MUB-triplet can be reconstructed from such a cube, up to unitary equivalence. We also present an algebraic identity which is conjectured to hold for all MUB-triplets in dimension 6. If true, it would imply the long-standing conjecture of Zauner that the maximum number of MUBs in dimension 6 is three.
Keywords
Cite
@article{arxiv.2503.14752,
title = {Triplets of Mutually Unbiased Bases},
author = {Máte Matolcsi and Ákos K. Matszangosz and Dániel Varga and Mihály Weiner},
journal= {arXiv preprint arXiv:2503.14752},
year = {2025}
}