Abstract
We study mutually unbiased bases in \({\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}\). A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in \({\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})\) 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.
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This work is supported by the NSFC under Numbers 11361065 and 11275131; the Natural Science Foundation of Jilin Province (201215239); the Natural Science Foundation of Yanbian University (2013, No. 17).
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Zhang, J., Tao, YH., Nan, H. et al. Construction of mutually unbiased bases in \({\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}\) . Quantum Inf Process 14, 2635–2644 (2015). https://doi.org/10.1007/s11128-015-0961-9
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DOI: https://doi.org/10.1007/s11128-015-0961-9