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Quantum Information Processing
Erschienen in: Quantum Information Processing 6/2015

01.06.2015

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

Erschienen in: Quantum Information Processing | Ausgabe 6/2015

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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 \((n+1)\)-qubit state \(\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right) \) from the partially entangled \((n+1)\)-qubit normalized state \(\alpha |\Psi _{0}\rangle |0\rangle +\beta |\Psi _{1}\rangle |1\rangle ,\) where \(\langle \Psi _{1}|\Psi _{0}\rangle =0\) and \(|\alpha |\ne \frac{1}{\sqrt{2}}\). 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 \(\frac{1}{\sqrt{2}}\left( |\Psi _{0}\rangle |0\rangle +|\Psi _{1}\rangle |1\rangle \right) \), 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.
Vorheriger Artikel Sudden death of distillability in a two-qutrit anisotropic Heisenberg spin model
Nächster Artikel Quantum differential cryptanalysis

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Fußnoten
1
In this paper, we have used \(|\psi ^{\pm }\rangle =\frac{|00\rangle \pm |11\rangle }{\sqrt{2}}\) and \(|\phi ^{\pm }\rangle =\frac{|01\rangle \pm |10\rangle }{\sqrt{2}}\). However, it may be noted that the opposite convention (i.e., \(|\phi ^{\pm }\rangle =\frac{|00\rangle \pm |11\rangle }{\sqrt{2}}\) and \(|\psi ^{\pm }\rangle =\frac{|01\rangle \pm |10\rangle }{\sqrt{2}}\)), is also frequently used in literature.
 
2
The swapping operation that changes the particle sequence as \(12345\rightarrow 15234\) can be viewed as a sequence of three conventional SWAP gates that work as follows: \(12345\rightarrow 15342\rightarrow 15243\rightarrow 15234\).
 
3
Here, \(U_{2,n+2}|\psi _{6}\rangle \) denotes that a single-qubit operation \(U_{2}\) operates on \((n+2)\)-th qubit of \(|\psi _{6}\rangle \) and identity operators operate on the rest of the qubits.
 
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Metadaten
Titel
Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states
Publikationsdatum
01.06.2015
Erschienen in
Quantum Information Processing / Ausgabe 6/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-015-0948-6

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