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The construction of mutually unbiased unextendible maximally entangled bases. (English) Zbl 1528.81082

Summary: Mutually unbiased bases (MUBs), a kind of important best measurement base, is widely applied to quantum information processing. In this paper, we obtain the different unextendible maximally entangled bases (UMEBs) by constructing unitary matrices in bipartite systems HCode \(C^d\otimes C^{d'}(\frac{d'}{2}< d< d')\). Then, we show that the sufficient and necessary conditions for UMEBs extend to MUBs in this bipartite systems. Finally, these results are generalized in bipartite systems \(C^d\otimes C^{d'}\) (\(d'=qd+r\), \(0<r<d\), \(q, r\in Z^+\)).

MSC:

81P55 Special bases (entangled, mutual unbiased, etc.)
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