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MiS Preprint
51/2018
Constructions of Unextendible Maximally Entangled Bases in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\)
We study unextendible maximally entangled bases (UMEBs) in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to construct $d(d'-1)$-number UMEBs is established, and two 25-member UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and \(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore, a systematic way of constructing $d(d'-r)$-number UMEBs in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) is presented for $r=1,2,\cdots, d-1$. Correspondingly, two UMEBs in \(\mathbb {C}^{3}\otimes \mathbb {C}^{10}\) are obtained.</p>
