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MiS Preprint
50/2015
Construction of Mutually Unbiased Bases in $\mathbb{C}^d\otimes \mathbb{C}^{2^ld'}$
Jun Zhang, Yuan-Hong Tao, Hua Nan and Shao-Ming Fei
Abstract
We study mutually unbiased bases in $\mathbb{C}^d\otimes \mathbb{C}^{2^ld'}$. A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $\mathbb{C}^d\otimes \mathbb{C}^{2^ld'} (l\in \mathbb{Z^+})$ from MUMEBs in $\mathbb{C}^d \otimes \mathbb{C}^{d'}(d'=kd, k\in \mathbb{Z}^+)$, and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $\mathbb{C}^d\otimes \mathbb{C}^{2^ld'} (l \in \mathbb{Z^+})$ from MUUMEBs in $\mathbb{C}^d \otimes \mathbb{C}^{d'}(d'=kd+r, 0<r<d)$ have been presented. Detailed examples are given.</p>
