Construction of mutually unbiased bases in \({\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}\)
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.
mutually unbiased bases maximally entangled states unextendible maximally entangled basis