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Erschienen in:
01.03.2017
Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices
Erschienen in: Quantum Information Processing | Ausgabe 3/2017
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Abstract
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.