English

All Mutually Unbiased Bases in Dimensions Two to Five

Mathematical Physics 2010-08-09 v2 math.MP Quantum Physics

Abstract

All complex Hadamard matrices in dimensions two to five are known. We use this fact to derive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We find a three-parameter family of triples of MU bases in dimension four and two inequivalent classes of MU triples in dimension five. We confirm that the complete sets of (d+1) MU bases are unique (up to equivalence) in dimensions below six, using only elementary arguments for d less than five.

Keywords

Cite

@article{arxiv.0907.4097,
  title  = {All Mutually Unbiased Bases in Dimensions Two to Five},
  author = {Stephen Brierley and Stefan Weigert and Ingemar Bengtsson},
  journal= {arXiv preprint arXiv:0907.4097},
  year   = {2010}
}

Comments

As the published version with minor changes

R2 v1 2026-06-21T13:28:17.859Z