# Indistinguishability of pure orthogonal product states by LOCC

Indistinguishability of pure orthogonal product states by LOCC We construct two sets of incomplete and extendible quantum pure orthogonal product states (POPS) in general bipartite high-dimensional quantum systems, which are all indistinguishable by local operations and classical communication. The first set of POPS is composed of two parts which are $$\mathcal {C}^m\otimes \mathcal {C}^{n_1}$$ C m ⊗ C n 1 with $$5\le m\le n_1$$ 5 ≤ m ≤ n 1 and $$\mathcal {C}^m\otimes \mathcal {C}^{n_2}$$ C m ⊗ C n 2 with $$5\le m \le n_2$$ 5 ≤ m ≤ n 2 , where $$n_1$$ n 1 is odd and $$n_2$$ n 2 is even. The second one is in $$\mathcal {C}^m\otimes \mathcal {C}^n$$ C m ⊗ C n $$(m, n\ge 4)$$ ( m , n ≥ 4 ) . Some subsets of these two sets can be extended into complete sets that local indistinguishability can be decided by noncommutativity which quantifies the quantumness of a quantum ensemble. Our study shows quantum nonlocality without entanglement. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Indistinguishability of pure orthogonal product states by LOCC

, Volume 16 (7) – May 22, 2017
17 pages

/lp/springer_journal/indistinguishability-of-pure-orthogonal-product-states-by-locc-PN6sl42ndq
Publisher
Springer US
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/s11128-017-1616-9
Publisher site
See Article on Publisher Site

### Abstract

We construct two sets of incomplete and extendible quantum pure orthogonal product states (POPS) in general bipartite high-dimensional quantum systems, which are all indistinguishable by local operations and classical communication. The first set of POPS is composed of two parts which are $$\mathcal {C}^m\otimes \mathcal {C}^{n_1}$$ C m ⊗ C n 1 with $$5\le m\le n_1$$ 5 ≤ m ≤ n 1 and $$\mathcal {C}^m\otimes \mathcal {C}^{n_2}$$ C m ⊗ C n 2 with $$5\le m \le n_2$$ 5 ≤ m ≤ n 2 , where $$n_1$$ n 1 is odd and $$n_2$$ n 2 is even. The second one is in $$\mathcal {C}^m\otimes \mathcal {C}^n$$ C m ⊗ C n $$(m, n\ge 4)$$ ( m , n ≥ 4 ) . Some subsets of these two sets can be extended into complete sets that local indistinguishability can be decided by noncommutativity which quantifies the quantumness of a quantum ensemble. Our study shows quantum nonlocality without entanglement.

### Journal

Quantum Information ProcessingSpringer Journals

Published: May 22, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations