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Quantum Information Processing

, Volume 14, Issue 6, pp 2077–2099 | Cite as

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

  • Chitra Shukla
  • Anindita Banerjee
  • Anirban PathakEmail author
Article

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.

Keywords

Entanglement concentration protocol (ECP) Quantum circuit Optical implementation of ECP 

Notes

Acknowledgments

AP thanks Department of Science and Technology (DST), India, for support provided through the DST Project No. SR/S2/LOP-0012/2010, and he also acknowledges the supports received from the Projects CZ.1.05/2.1.00/03.0058 and CZ.1.07/2.3.00/20.0017 of the Ministry of Education, Youth and Sports of the Czech Republic. The authors also thank Dr. Alessio Avella for his inputs on the possibility of the experimental realizations of the proposed protocols.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chitra Shukla
    • 1
  • Anindita Banerjee
    • 2
  • Anirban Pathak
    • 1
    • 3
    Email author
  1. 1.Jaypee Institute of Information TechnologyNoidaIndia
  2. 2.Department of Physics and Center for Astroparticle Physics and Space ScienceBose InstituteKolkataIndia
  3. 3.RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of SciencePalacky UniversityOlomoucCzech Republic

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