# Multipartite unextendible entangled basis

Multipartite unextendible entangled basis The unextendible entangled basis with any arbitrarily given Schmidt number k (UEBk) in $${\mathbb {C}}^{d_1}\otimes {\mathbb {C}}^{d_2}$$ C d 1 ⊗ C d 2 is proposed in Guo and Wu (Phys Rev A 90:054303, 2014), $$1<k\le \min \{d_1,d_2\}$$ 1 < k ≤ min { d 1 , d 2 } , which is a set of orthonormal entangled states with Schmidt number k in a $$d_1\otimes d_2$$ d 1 ⊗ d 2 system consisting of fewer than $$d_1d_2$$ d 1 d 2 vectors which have no additional entangled vectors with Schmidt number k in the complementary space. In this paper, we extend it to multipartite case, and a general way of constructing $$(m+1)$$ ( m + 1 ) -partite UEBk from m-partite UEBk is proposed ( $$m\ge 2$$ m ≥ 2 ). Consequently, we show that there are infinitely many UEBks in $${\mathbb {C}}^{d_1}\otimes {\mathbb {C}}^{d_2}\otimes \cdots \otimes {\mathbb {C}}^{d_N}$$ C d 1 ⊗ C d 2 ⊗ ⋯ ⊗ C d N with any dimensions and any $$N\ge 3$$ N ≥ 3 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Multipartite unextendible entangled basis

, Volume 14 (9) – Jul 2, 2015
16 pages
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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
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/s11128-015-1058-1
Publisher site
See Article on Publisher Site

### Abstract

The unextendible entangled basis with any arbitrarily given Schmidt number k (UEBk) in $${\mathbb {C}}^{d_1}\otimes {\mathbb {C}}^{d_2}$$ C d 1 ⊗ C d 2 is proposed in Guo and Wu (Phys Rev A 90:054303, 2014), $$1<k\le \min \{d_1,d_2\}$$ 1 < k ≤ min { d 1 , d 2 } , which is a set of orthonormal entangled states with Schmidt number k in a $$d_1\otimes d_2$$ d 1 ⊗ d 2 system consisting of fewer than $$d_1d_2$$ d 1 d 2 vectors which have no additional entangled vectors with Schmidt number k in the complementary space. In this paper, we extend it to multipartite case, and a general way of constructing $$(m+1)$$ ( m + 1 ) -partite UEBk from m-partite UEBk is proposed ( $$m\ge 2$$ m ≥ 2 ). Consequently, we show that there are infinitely many UEBks in $${\mathbb {C}}^{d_1}\otimes {\mathbb {C}}^{d_2}\otimes \cdots \otimes {\mathbb {C}}^{d_N}$$ C d 1 ⊗ C d 2 ⊗ ⋯ ⊗ C d N with any dimensions and any $$N\ge 3$$ N ≥ 3 .

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 2, 2015

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