# Entanglement of four-qubit rank-2 mixed states

Entanglement of four-qubit rank-2 mixed states It is known that there are three maximally entangled states $$|\varPhi _1 \rangle = (|0000 \rangle + |1111 \rangle ) / \sqrt{2}$$ | Φ 1 ⟩ = ( | 0000 ⟩ + | 1111 ⟩ ) / 2 , $$|\varPhi _2 \rangle = (\sqrt{2} |1111 \rangle + |1000 \rangle + |0100 \rangle + |0010 \rangle + |0001 \rangle ) / \sqrt{6}$$ | Φ 2 ⟩ = ( 2 | 1111 ⟩ + | 1000 ⟩ + | 0100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 6 , and $$|\varPhi _3 \rangle = (|1111 \rangle + |1100 \rangle + |0010 \rangle + |0001 \rangle ) / 2$$ | Φ 3 ⟩ = ( | 1111 ⟩ + | 1100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 2 in four-qubit system. It is also known that there are three independent measures $$\mathcal{F}^{(4)}_j (j=1,2,3)$$ F j ( 4 ) ( j = 1 , 2 , 3 ) for true four-way quantum entanglement in the same system. In this paper, we compute $$\mathcal{F}^{(4)}_j$$ F j ( 4 ) and their corresponding linear monotones $$\mathcal{G}^{(4)}_j$$ G j ( 4 ) for three rank-two mixed states $$\rho _j = p |\varPhi _j \rangle \langle \varPhi _j | + (1 - p) |\text{ W }_4 \rangle \langle \text{ W }_4 |$$ ρ j = p | Φ j ⟩ ⟨ Φ j | + ( 1 - p ) | W 4 ⟩ ⟨ W 4 | , where $$|\text{ W }_4 \rangle = (|0111 \rangle + |1011 \rangle + |1101 \rangle + |1110 \rangle ) / 2$$ | W 4 ⟩ = ( | 0111 ⟩ + | 1011 ⟩ + | 1101 ⟩ + | 1110 ⟩ ) / 2 . We discuss the possible applications of our results briefly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Entanglement of four-qubit rank-2 mixed states

, Volume 14 (9) – Jun 11, 2015
17 pages

/lp/springer_journal/entanglement-of-four-qubit-rank-2-mixed-states-vT14SpSyaW
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/s11128-015-1039-4
Publisher site
See Article on Publisher Site

### Abstract

It is known that there are three maximally entangled states $$|\varPhi _1 \rangle = (|0000 \rangle + |1111 \rangle ) / \sqrt{2}$$ | Φ 1 ⟩ = ( | 0000 ⟩ + | 1111 ⟩ ) / 2 , $$|\varPhi _2 \rangle = (\sqrt{2} |1111 \rangle + |1000 \rangle + |0100 \rangle + |0010 \rangle + |0001 \rangle ) / \sqrt{6}$$ | Φ 2 ⟩ = ( 2 | 1111 ⟩ + | 1000 ⟩ + | 0100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 6 , and $$|\varPhi _3 \rangle = (|1111 \rangle + |1100 \rangle + |0010 \rangle + |0001 \rangle ) / 2$$ | Φ 3 ⟩ = ( | 1111 ⟩ + | 1100 ⟩ + | 0010 ⟩ + | 0001 ⟩ ) / 2 in four-qubit system. It is also known that there are three independent measures $$\mathcal{F}^{(4)}_j (j=1,2,3)$$ F j ( 4 ) ( j = 1 , 2 , 3 ) for true four-way quantum entanglement in the same system. In this paper, we compute $$\mathcal{F}^{(4)}_j$$ F j ( 4 ) and their corresponding linear monotones $$\mathcal{G}^{(4)}_j$$ G j ( 4 ) for three rank-two mixed states $$\rho _j = p |\varPhi _j \rangle \langle \varPhi _j | + (1 - p) |\text{ W }_4 \rangle \langle \text{ W }_4 |$$ ρ j = p | Φ j ⟩ ⟨ Φ j | + ( 1 - p ) | W 4 ⟩ ⟨ W 4 | , where $$|\text{ W }_4 \rangle = (|0111 \rangle + |1011 \rangle + |1101 \rangle + |1110 \rangle ) / 2$$ | W 4 ⟩ = ( | 0111 ⟩ + | 1011 ⟩ + | 1101 ⟩ + | 1110 ⟩ ) / 2 . We discuss the possible applications of our results briefly.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 11, 2015

## 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