paper

Constructing mutually unbiased bases from unextendible maximally entangled bases

arXiv:2001.09515 · doi:10.1016/S0034-4877(20)30013-6

Abstract

We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^{2} \otimes C^{4}$ . Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in $C^{2} \otimes C^{4}$ . The results are generalized to $C^{2} \otimes C^{d}$ $(d \geq 3)$ and a concrete example in $C^{2} \otimes C^{8}$ is given.

14 pages