Mutually unbiased bases in dimension six containing a product-vector basis
Quantum Physics
2018-07-13 v2
Abstract
Excluding the existence of four MUBs in is an open problem in quantum information. We investigate the number of product vectors in the set of four mutually unbiased bases (MUBs) in dimension six, by assuming that the set exists and contains a product-vector basis. We show that in most cases the number of product vectors in each of the remaining three MUBs is at most two. We further construct the exceptional case in which the three MUBs respectively contain at most three, two and two product vectors. We also investigate the number of vectors mutually unbiased to an orthonormal basis.
Keywords
Cite
@article{arxiv.1706.00311,
title = {Mutually unbiased bases in dimension six containing a product-vector basis},
author = {Lin Chen and Li Yu},
journal= {arXiv preprint arXiv:1706.00311},
year = {2018}
}
Comments
10 pages, the total number of vectors in the introduction and the conclusion was revised. arXiv admin note: text overlap with arXiv:1610.04875