English

Mutually unbiased bases for quantum states defined over p-adic numbers

Quantum Physics 2011-09-02 v1

Abstract

We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known. We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces.

Keywords

Cite

@article{arxiv.1109.0060,
  title  = {Mutually unbiased bases for quantum states defined over p-adic numbers},
  author = {Wim van Dam and Alexander Russell},
  journal= {arXiv preprint arXiv:1109.0060},
  year   = {2011}
}

Comments

11 pages

R2 v1 2026-06-21T18:58:07.905Z