# Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states

Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like... Three entanglement concentration protocols (ECPs) are proposed. The first ECP and a modified version of that are shown to be useful for the creation of maximally entangled cat and GHZ-like states from their non-maximally entangled counterparts. The last two ECPs are designed for the creation of maximally entangled $$(n+1)$$ ( n + 1 ) -qubit state $$\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right)$$ 1 2 | Ψ 0 ⟩ | 0 ⟩ + | Ψ 1 ⟩ | 1 ⟩ from the partially entangled $$(n+1)$$ ( n + 1 ) -qubit normalized state $$\alpha |\Psi _{0}\rangle |0\rangle +\beta |\Psi _{1}\rangle |1\rangle ,$$ α | Ψ 0 ⟩ | 0 ⟩ + β | Ψ 1 ⟩ | 1 ⟩ , where $$\langle \Psi _{1}|\Psi _{0}\rangle =0$$ ⟨ Ψ 1 | Ψ 0 ⟩ = 0 and $$|\alpha |\ne \frac{1}{\sqrt{2}}$$ | α | ≠ 1 2 . It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the nine SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as $$\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right)$$ 1 2 | Ψ 0 ⟩ | 0 ⟩ + | Ψ 1 ⟩ | 1 ⟩ , and consequently, the last two ECPs proposed here are applicable to all these states. Quantum circuits for the implementation of the proposed ECPs are provided, and it is shown that the proposed ECPs can be realized using linear optics. The efficiency of the ECPs is studied using a recently introduced quantitative measure (Sheng et al., Phys Rev A 85:012307, 2012). Limitations of the measure are also reported. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states

, Volume 14 (6) – Feb 19, 2015
23 pages

/lp/springer_journal/protocols-and-quantum-circuits-for-implementing-entanglement-N7b5jGtzbv
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/s11128-015-0948-6
Publisher site
See Article on Publisher Site

### Abstract

Three entanglement concentration protocols (ECPs) are proposed. The first ECP and a modified version of that are shown to be useful for the creation of maximally entangled cat and GHZ-like states from their non-maximally entangled counterparts. The last two ECPs are designed for the creation of maximally entangled $$(n+1)$$ ( n + 1 ) -qubit state $$\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right)$$ 1 2 | Ψ 0 ⟩ | 0 ⟩ + | Ψ 1 ⟩ | 1 ⟩ from the partially entangled $$(n+1)$$ ( n + 1 ) -qubit normalized state $$\alpha |\Psi _{0}\rangle |0\rangle +\beta |\Psi _{1}\rangle |1\rangle ,$$ α | Ψ 0 ⟩ | 0 ⟩ + β | Ψ 1 ⟩ | 1 ⟩ , where $$\langle \Psi _{1}|\Psi _{0}\rangle =0$$ ⟨ Ψ 1 | Ψ 0 ⟩ = 0 and $$|\alpha |\ne \frac{1}{\sqrt{2}}$$ | α | ≠ 1 2 . It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the nine SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as $$\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right)$$ 1 2 | Ψ 0 ⟩ | 0 ⟩ + | Ψ 1 ⟩ | 1 ⟩ , and consequently, the last two ECPs proposed here are applicable to all these states. Quantum circuits for the implementation of the proposed ECPs are provided, and it is shown that the proposed ECPs can be realized using linear optics. The efficiency of the ECPs is studied using a recently introduced quantitative measure (Sheng et al., Phys Rev A 85:012307, 2012). Limitations of the measure are also reported.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 19, 2015

### References

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Yu, C-S; Song, H-S

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