Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices

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• 作者：Dengming xu
• 关键词：Mutually unbiased bases ; Mutually unbiased maximally entangled states ; Pauli operators ; Permutation matrices ; Hardamard matrices ; Galois rings
• 刊名：Quantum Information Processing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：16
• 期：3
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics;
• 出版者：Springer US
• ISSN：1573-1332
• 卷排序：16

文摘

We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system \({\mathbb {C}}^d\otimes {\mathbb {C}}^d (d\ge 3)\) with d a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct \(2(d-1)\) MUMEBs in \({\mathbb {C}}^d\otimes {\mathbb {C}}^d\). It follows that \(M(d,d)\ge 2(d-1)\), which is twice the number given in Liu et al. (2016), where M(d, d) denotes the maximal size of all sets of MUMEBs in \({\mathbb {C}}^d\otimes {\mathbb {C}}^d\). In addition, let q be another power of a prime number, we construct MUMEBs in \({\mathbb {C}}^d\otimes {\mathbb {C}}^{qd}\) from those in \({\mathbb {C}}^d\otimes {\mathbb {C}}^d\) by the use of the tensor product of unitary matrices.