# Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^d$$ C d ⊗ C d

Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^d$$ C d... We study mutually unbiased maximally entangled bases (MUMEB’s) in bipartite system $$\mathbb {C}^d\otimes \mathbb {C}^d (d \ge 3)$$ C d ⊗ C d ( d ≥ 3 ) . We generalize the method to construct MUMEB’s given in Tao et al. (Quantum Inf Process 14:2291–2300, 2015), by using any commutative ring R with d elements and generic character of $$(R,+)$$ ( R , + ) instead of $$\mathbb {Z}_d=\mathbb {Z}/d\mathbb {Z}$$ Z d = Z / d Z . Particularly, if $$d=p_1^{a_1}p_2^{a_2}\ldots p_s^{a_s}$$ d = p 1 a 1 p 2 a 2 … p s a s where $$p_1, \ldots , p_s$$ p 1 , … , p s are distinct primes and $$3\le p_1^{a_1}\le \cdots \le p_s^{a_s}$$ 3 ≤ p 1 a 1 ≤ ⋯ ≤ p s a s , we present $$p_1^{a_1}-1$$ p 1 a 1 - 1 MUMEB’s in $$\mathbb {C}^d\otimes \mathbb {C}^d$$ C d ⊗ C d by taking $$R=\mathbb {F}_{p_1^{a_1}}\oplus \cdots \oplus \mathbb {F}_{p_s^{a_s}}$$ R = F p 1 a 1 ⊕ ⋯ ⊕ F p s a s , direct sum of finite fields (Theorem 3.3). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^d$$ C d ⊗ C d

, Volume 16 (6) – May 9, 2017
8 pages

/lp/springer_journal/mutually-unbiased-maximally-entangled-bases-in-mathbb-c-d-otimes-i0WlokwoWX
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/s11128-017-1608-9
Publisher site
See Article on Publisher Site

### Abstract

We study mutually unbiased maximally entangled bases (MUMEB’s) in bipartite system $$\mathbb {C}^d\otimes \mathbb {C}^d (d \ge 3)$$ C d ⊗ C d ( d ≥ 3 ) . We generalize the method to construct MUMEB’s given in Tao et al. (Quantum Inf Process 14:2291–2300, 2015), by using any commutative ring R with d elements and generic character of $$(R,+)$$ ( R , + ) instead of $$\mathbb {Z}_d=\mathbb {Z}/d\mathbb {Z}$$ Z d = Z / d Z . Particularly, if $$d=p_1^{a_1}p_2^{a_2}\ldots p_s^{a_s}$$ d = p 1 a 1 p 2 a 2 … p s a s where $$p_1, \ldots , p_s$$ p 1 , … , p s are distinct primes and $$3\le p_1^{a_1}\le \cdots \le p_s^{a_s}$$ 3 ≤ p 1 a 1 ≤ ⋯ ≤ p s a s , we present $$p_1^{a_1}-1$$ p 1 a 1 - 1 MUMEB’s in $$\mathbb {C}^d\otimes \mathbb {C}^d$$ C d ⊗ C d by taking $$R=\mathbb {F}_{p_1^{a_1}}\oplus \cdots \oplus \mathbb {F}_{p_s^{a_s}}$$ R = F p 1 a 1 ⊕ ⋯ ⊕ F p s a s , direct sum of finite fields (Theorem 3.3).

### Journal

Quantum Information ProcessingSpringer Journals

Published: May 9, 2017

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