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Maximal entanglement concentration for a set of \((n+1)\)-qubit states

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Abstract

We propose two schemes for concentration of \((n+1)\)-qubit entangled states that can be written in the form of \(\left( \alpha |\varphi _{0}\rangle |0\rangle +\beta |\varphi _{1}\rangle |1\rangle \right) _{n+1}\) where \(|\varphi _{0}\rangle \) and \(|\varphi _{1}\rangle \) are mutually orthogonal n-qubit states. The importance of this general form is that the entangled states such as Bell, cat, GHZ, GHZ-like, \(|\varOmega \rangle \), \(|Q_{5}\rangle \), 4-qubit cluster states and specific states from the nine SLOCC-nonequivalent families of 4-qubit entangled states can be expressed in this form. The proposed entanglement concentration protocol is based on the local operations and classical communications (LOCC). It is shown that the maximum success probability for ECP using quantum nondemolition technique (QND) is \(2\beta ^{2}\) for \((n+1)\)-qubit states of the prescribed form. It is shown that the proposed schemes can be implemented optically. Further, it is also noted that the proposed schemes can be implemented using quantum dot and microcavity systems.

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Acknowledgments

AB thanks DST-SERB Project SR/S2/LOP-18/2012. AB also acknowledges S. Bandyopadhyay for some technical discussion and his interest in the present work. AP thanks Department of Science and Technology (DST), India, for support provided through the DST Project No. SR/S2/LOP-0012/2010. CS thanks to Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for JSPS Fellows no. 15F15015.

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Authors and Affiliations

  1. Department of Physics and Center for Astroparticle Physics and Space Science, Bose Institute, Block EN, Sector V, Kolkata, India

    Anindita Banerjee

  2. Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

    Chitra Shukla

  3. Department of Physics and Materials Science and Engineering, Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP, 201307, India

    Anirban Pathak

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  1. Anindita Banerjee
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  2. Chitra Shukla
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Correspondence to Anindita Banerjee.

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Banerjee, A., Shukla, C. & Pathak, A. Maximal entanglement concentration for a set of \((n+1)\)-qubit states. Quantum Inf Process 14, 4523–4536 (2015). https://doi.org/10.1007/s11128-015-1128-4

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  • DOI: https://doi.org/10.1007/s11128-015-1128-4

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