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

Construction of mutually unbiased maximally entangled bases through permutations of Hadamard... We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system $${\mathbb {C}}^d\otimes {\mathbb {C}}^d (d\ge 3)$$ C d ⊗ C d ( d ≥ 3 ) with d a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct $$2(d-1)$$ 2 ( d - 1 ) MUMEBs in $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d . It follows that $$M(d,d)\ge 2(d-1)$$ M ( d , d ) ≥ 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 $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d . In addition, let q be another power of a prime number, we construct MUMEBs in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{qd}$$ C d ⊗ C q d from those in $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d by the use of the tensor product of unitary matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

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

, Volume 16 (3) – Feb 2, 2017
11 pages

/lp/springer_journal/construction-of-mutually-unbiased-maximally-entangled-bases-through-8vkmOMxIR9
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1534-x
Publisher site
See Article on Publisher Site

### Abstract

We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system $${\mathbb {C}}^d\otimes {\mathbb {C}}^d (d\ge 3)$$ C d ⊗ C d ( d ≥ 3 ) with d a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct $$2(d-1)$$ 2 ( d - 1 ) MUMEBs in $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d . It follows that $$M(d,d)\ge 2(d-1)$$ M ( d , d ) ≥ 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 $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d . In addition, let q be another power of a prime number, we construct MUMEBs in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{qd}$$ C d ⊗ C q d from those in $${\mathbb {C}}^d\otimes {\mathbb {C}}^d$$ C d ⊗ C d by the use of the tensor product of unitary matrices.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 2, 2017

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