Constructing mutually unbiased bases from unextendible maximally entangled bases

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 $C^2\otimes C^d$ $(d\ge 3)$ and a concrete example in $C^2\otimes C^8$ is given.

arXiv comment14 pages

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