Advertisement

Quantum Information Processing

, Volume 12, Issue 1, pp 205–215 | Cite as

Construction of four-qubit quantum entanglement for SI (S = 3/2, I = 3/2) spin system

  • Ahmet Gün
  • Selçuk Çakmak
  • Azmi Gençten
Article

Abstract

In quantum information processing, spin-3/2 electron or nuclear spin states are known as two-qubit states. For SI (S = 3/2, I = 3/2) spin system, there are 16 four-qubit states. In this study, first, four-qubit entangled states are obtained by using the matrix representation of Hadamard and CNOT logic gates. By considering 75As@C60 molecule as SI (S = 3/2, I = 3/2) spin system, four-qubit entangled states are also obtained by using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates. Then, it is shown that obtained entangled states can be transformed into each other by the transformation operators.

Keywords

Four-qubit states Four-qubit CNOT Quantum entanglement Endohedral fullerenes Magnetic resonance selective pulses 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, UK (2001)Google Scholar
  2. 2.
    DiVincenzo D.P.: Quantum computation. Science 270, 255–261 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Loyd S.: Quantum-mechanical computers. Sci. Am. 273, 140–145 (1995)CrossRefGoogle Scholar
  4. 4.
    Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Bell J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)Google Scholar
  6. 6.
    Furman G.B., Meerovich V.M., Sokolovsky V.L.: Entanglement in nuclear quadrupole resonance. Hyperfine Interact 198, 153–159 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    Bethune D.S., Johnson R.D., Salem J.R., Devries M.S., Yannoni C.S.: Atoms in carbon cages—the structure and properties of endohedral fullerenes. Nature 366, 123–128 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    Wakabayashi T.: Fullerene C 60: a possible molecular computer. In: Nakahara, M., Ota, Y., Rahimi, R., Kondo, Y., Tada-Umezaki, M. (eds) Molecular Realizations of Quantum Computing 2007, pp. 163–192. World Scientific Publishing Co. Pte. Ltd. Kinki Univ., Japan (2009)CrossRefGoogle Scholar
  9. 9.
    Heidebrecht A., Mende J., Mehring M.: Quantum state engineering with spins. Fortschr. Phys. 54, 788–803 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Feng M., Twamley J.: Selective pulse implementation of two-qubit gates for spin-3/2-based fullerene quantum-information processing. Phys. Rev. A 70, 032318 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Ju C., Suter D., Du J.: Two-qubit gates between noninteracting qubits in endohedral-fullerene-based quantum computation. Phys. Rev. A 75, 012318 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Mehring M., Scherer W., Weidinger A.: Pseudoentanglement of spin states in the multilevel 15 N@C60 system. Phys. Rev. Lett. 93, 206603 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    Harneit W.: Fullerene-based electron-spin quantum computer. Phys. Rev. A 65, 032322 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    Suter D., Lim K.: Scalable architecture for spin-based quantum computers with a single type of gate. Phys. Rev. A 65, 052309 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Mehring M., Mende J., Scherer W.: Entanglement between an electron and a nuclear spin 1/2. Phys. Rev. Lett. 90, 153001 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    Scherer W., Mehring M.: Entagled electron and nuclear spin states in 15 N@C 60: density matrix tomography. J. Chem. Phys. 128, 052305 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    Yang W.L., Xu Z.Y., Wei H., Feng M., Suter D.: Quantum–information–processing architecture with endohedral fullerenes in a carbon nanotube. Phys. Rev. A 81, 032303 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Sato K., Nakazawa S., Rahimi R.D., Nishida S., Ise T., Shimoi D., Toyota K., Morita Y., Kitagawa M., Carl P., Höfner P., Takui T.: Quantum computing using pulse-based electron-nuclear double resonance (ENDOR): molecular spin-qubits. In: Nakahara, M., Ota, Y., Rahimi, R., Kondo, Y., Tada-Umezaki, M. (eds) Molecular Realizations of Quantum Computing 2007, pp. 59–162. World Scientific Publishing Co. Pte. Ltd. Kinki Univ., Japan (2009)Google Scholar
  19. 19.
    Twamley J.: Quantum–cellular–automata quantum computing with endohedral fullerenes. Phys. Rev. A 67, 052318 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Ju C., Suter D., Du J.: Two-qubit gates between noninteracting qubits in endohedral-fullerene-based quantum computation. Phys. Rev. A 75, 012318 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    Rahimi R., Sato K., Shiomi D., Takui T.: Quantum information processing as studied by molecule-based pulsed ENDOR spectroscopy. In: Graham, A.W. (eds) Modern Magnetic Resonance, pp. 643–650. Springer, Netherlands (2006)Google Scholar
  22. 22.
    Oliveira I.S., Bonagamba T.J., Sarthour R.S., Freitas J.C.C., deAzevede E.R.: NMR Quantum Information Processing. Elsevier, Netherlands (2007)Google Scholar
  23. 23.
    Bonk F.A., deAzevedo E.R., Sarthour R.S., Bulnes J.D., Freitas J.C.C., Guimaraes A.P., Oliveira I.S., Bonagamba T.J.: Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography. J. Magn. Reson. 175, 226–234 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    Kesel A.R., Ermakov V.L.: Multiqubit spin. JETP Lett. 70, 61–65 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    Gün A., Şaka İ., Gençten A.: Construction and application of four-qubit SWAP logic gate in NMR quantum computing. Int. J. Quantum Inf. 9, 779–790 (2011)MATHCrossRefGoogle Scholar
  26. 26.
    BelBruno J.J.: Computational study of N@C60, P@C60, and As@C60. Fuller. Nanotub. Carbon Nanostruct. 10, 23–35 (2002)CrossRefGoogle Scholar
  27. 27.
    Liu X.S., Long G.L., Tong D.M., Li F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65, 022304 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Vega A.J.: CP/MAS of quadrupolar S = 3/2 nuclei. Solid State Nuclear Magn. Reson. 1, 17–32 (1992)CrossRefGoogle Scholar
  29. 29.
    Vega A.J.: MAS NMR spin locking of half-integer quadrupolar nuclei. J. Magn. Reson. 96, 50–68 (1992)Google Scholar
  30. 30.
    Kao H.M., Grey C.P.: INEPT experiments involving quadrupolar nuclei in solids. J. Magn. Reson. 133, 313–323 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Arts and SciencesOndokuz Mayıs UniversitySamsunTurkey

Personalised recommendations