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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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References

  1. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  2. Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194 (1999)

    Article  ADS  Google Scholar 

  3. Bandyopadhyay, S.: Qubit- and entanglement-assisted optimal entanglement concentration. Phys. Rev. A 62, 032308 (2000)

    Article  ADS  Google Scholar 

  4. Gu, Y.J., Li, W.D., Guo, G.C.: Protocol and quantum circuits for realizing deterministic entanglement concentration. Phys. Rev. A 73, 022321 (2006)

    Article  ADS  Google Scholar 

  5. Lee, S.W., Jeong, H.: Near-deterministic quantum teleportation and resource-efficient quantum computation usinglinear optics and hybrid qubits. Phys. Rev. A 87, 022326 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  6. Choudhury, B.S., Dhara, A.: A three-qubit state entanglement concentration protocol assisted by two-qubit systems. Int. J. Theor. Phys. 52, 3965 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Shukla, C., Banerjee, A., Pathak, A.: Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states. Quantum Inf. Process. 14, 2077 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  8. Choudhury, B.S., Dhara, A.: An entanglement concentration protocol for cluster states. Quantum Inf. Process. 12, 2577 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Lan, Z.: Consequent entanglement concentration of a less-entangled electronic cluster state with controlled-not gates. Chin. Phys. B 23, 050308 (2014)

    Article  ADS  Google Scholar 

  10. Zhao, S.Y., Liu, J., Zhou, L., Sheng, Y.B.: Two-step entanglement concentration for arbitrary electronic cluster state. Quantum Inf. Process. 12, 3633 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  12. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  13. Zhao, Z., Yang, T., Chen, Y.A., Zhang, A.N., Pan, J.W.: Experimental realization of entanglement concentration and a quantum repeater. Phys. Rev. Lett. 90, 207901 (2003)

    Article  ADS  Google Scholar 

  14. Yamamoto, T., Koashi, M., Ozdemir, S.K., Imoto, N.: Experimental extraction of an entangled photon pair from two identically decohered pairs. Nature 421, 343 (2003)

    Article  ADS  Google Scholar 

  15. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  16. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  17. Wang, C.: Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys. Rev. A 86, 012323 (2012)

    Article  ADS  Google Scholar 

  18. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  19. Sheng, Y.B., Zhou, L., Wang, L., Zhao, S.M.: Efficient entanglement concentration for quantum dot and optical microcavities systems. Quantum Inf. Process. 12, 1885 (2013)

    Article  ADS  MATH  Google Scholar 

  20. Sheng, Y.B., Liu, J., Zhao, S.Y., Zhou, L.: Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system. Chin. Sci. Bull. 58, 3507 (2013)

    Article  Google Scholar 

  21. Ren, B.C., Wei, H.R., Li, T., Hua, M., Deng, F.G.: Optimal multipartite entanglement concentration of electron-spin states based on charge detection and projection measurements. Quantum Inf. Process. 13, 825 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.M.: Efficient entanglement concentration for arbitrary single-photon multimode W state. J. Opt. Soc. Am. B 30, 71 (2013)

    Article  ADS  Google Scholar 

  23. Rigas, I., Klimov, A.B., Sanchez-Soto, L.L., Leuchs, G.: Nonlinear cross-Kerr quasiclassical dynamics. New J. Phys. 15, 043038 (2013)

    Article  ADS  Google Scholar 

  24. Cao, C., Wang, C., He, L.Y., Zhang, R.: Atomic entanglement purification and concentration using coherent state input–output process in low-Q cavity QED regime. Opt. Express 21(Issue 4), 4093 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  25. Zhou, L.: Efficient entanglement concentration for electron-spin W state with the charge detection. Quantum Inf. Process. 12(Issue 6), 2087 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Zhou, L., Wang, X.F., Sheng, Y.B.: Efficient entanglement concentration for arbitrary less-entangled N-atom GHZ state. Int. J. Theor. Phys. 53, 1752 (2014)

    Article  MATH  Google Scholar 

  27. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.-M.: Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Inf. Process. 12, 1307 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Sheng, Y.B., Zhou, L.: Efficient W-state entanglement concentration using quantum-dot and optical microcavities. JOSA B 30(Issue 3), 678 (2013)

    Article  ADS  Google Scholar 

  29. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.M.: Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Inf. Process. 12, 1307 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Hea, L.Y., Cao, C., Wang, C.: Entanglement concentration for multi-particle partially entangled W state using nitrogen vacancy center and microtoroidal resonator system. Opt. Commun. 298, 260 (2013)

  31. Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Mishra, S., Shukla, C., Pathak, A., Srikanth, R., Venugopalan, A.: An integrated hierarchical dynamic quantum secret sharing protocol. Int. J. Theor. Phys. 54, 3143 (2015)

    Article  Google Scholar 

  33. Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)

    Article  ADS  Google Scholar 

  34. Munro, W.J., Nemoto, K., Spiller, T.P.: Weak nonlinearities: a new route to optical quantum computation. New J. Phys. 7, 137 (2005)

    Article  ADS  Google Scholar 

  35. Barrett, S.D., Kok, P., Nemoto, K., Beausoleil, R.G., Munro, W.J., Spiller, T.P.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71, 060302 (2005)

    Article  ADS  Google Scholar 

  36. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  37. Lo, H.K., Popescu, S.: Concentrating entanglement by local actions: Beyond mean values. Phys. Rev. A 63, 022301 (2001)

    Article  ADS  Google Scholar 

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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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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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