Constructing mutually unbiased bases from unextendible maximally entangled bases

Hui Zhao, Lin Zhang, Shao-Ming Fei, and Naihuan Jing

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Submission date: 21. Aug. 2019
Pages: 19
published in: Reports on mathematical physics, 85 (2020) 1, p. 105-118 
DOI number (of the published article): 10.1016/S0034-4877(20)30013-6
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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 C² ⊗ C⁴. Based on this condition, an analytical necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in C² ⊗ C⁴. The results are generalized to C² ⊗ C^d (d ≥ 3) and a concrete example in C² ⊗ C⁸ is given.