Abstract

We propose a scheme to realize a special quantum cloning machine (QCM) in cavity quantum electrodynamics (QED). The QCM can copy the information from one atom to another two distant atoms trapped in cavity QED with the help of a single-photon pulse. By choosing different parameters, we can perform an optimal symmetry 12 real state QCM and an optimal symmetry 13 economical real state QCM.

© 2011 Optical Society of America

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  1. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
    [CrossRef]
  2. D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
    [CrossRef]
  3. V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
    [CrossRef] [PubMed]
  4. D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
    [CrossRef]
  5. W. H. Zhang, T. Wu, L. Ye, and J. L. Dai, “Optimal real state cloning in d dimensions,” Phys. Rev. A 75, 044303–044307(2007);
    [CrossRef]
  6. W. H. Zhang and L. Ye, “Optimal asymmetric phase-covariant and real state cloning in d dimensions,” New J. Phys. 9, 318–332(2007).
    [CrossRef]
  7. T. Durt and J. Du, “Characterization of low-cost one-to-two qubit cloning,” Phys. Rev. A 69, 062316–062326 (2004).
    [CrossRef]
  8. Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
    [CrossRef] [PubMed]
  9. H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317–012322 (2007).
    [CrossRef]
  10. M. Sabuncu, U. L. Andersen, and G. Leuchs, “Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503–170507 (2007).
    [CrossRef]
  11. M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312–052317 (2008).
    [CrossRef]
  12. J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
    [CrossRef]
  13. A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
    [CrossRef] [PubMed]
  14. J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
    [CrossRef]
  15. Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger—Horne—Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127–021130 (2008).
    [CrossRef]
  16. C. S. Yu, X. X. Yi, H. S.Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301–044305 (2007).
    [CrossRef]
  17. X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
    [CrossRef]
  18. Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
    [CrossRef]
  19. Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304–064308 (2009).
    [CrossRef]
  20. C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
    [CrossRef] [PubMed]
  21. L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902–127906 (2004).
    [CrossRef] [PubMed]
  22. P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
    [CrossRef] [PubMed]

2009

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304–064308 (2009).
[CrossRef]

2008

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312–052317 (2008).
[CrossRef]

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger—Horne—Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127–021130 (2008).
[CrossRef]

2007

C. S. Yu, X. X. Yi, H. S.Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301–044305 (2007).
[CrossRef]

W. H. Zhang, T. Wu, L. Ye, and J. L. Dai, “Optimal real state cloning in d dimensions,” Phys. Rev. A 75, 044303–044307(2007);
[CrossRef]

W. H. Zhang and L. Ye, “Optimal asymmetric phase-covariant and real state cloning in d dimensions,” New J. Phys. 9, 318–332(2007).
[CrossRef]

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317–012322 (2007).
[CrossRef]

M. Sabuncu, U. L. Andersen, and G. Leuchs, “Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503–170507 (2007).
[CrossRef]

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

2006

X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
[CrossRef]

2005

Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

2004

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902–127906 (2004).
[CrossRef] [PubMed]

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

T. Durt and J. Du, “Characterization of low-cost one-to-two qubit cloning,” Phys. Rev. A 69, 062316–062326 (2004).
[CrossRef]

2002

A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef] [PubMed]

2001

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

2000

D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
[CrossRef]

1996

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef] [PubMed]

1982

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[CrossRef]

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[CrossRef]

Andersen, U. L.

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312–052317 (2008).
[CrossRef]

M. Sabuncu, U. L. Andersen, and G. Leuchs, “Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503–170507 (2007).
[CrossRef]

Bartušková, L.

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Bouwmeester, D.

A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

Bruß, D.

D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
[CrossRef]

Bužek, V.

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef] [PubMed]

Cernoch, A.

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Chen, H. W.

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317–012322 (2007).
[CrossRef]

Chen, Q.

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304–064308 (2009).
[CrossRef]

Chen, Y. A.

Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
[CrossRef] [PubMed]

Choi, K. S.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Chou, C. W.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Cinchetti, M.

D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
[CrossRef]

D’Ariano, G. M.

D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
[CrossRef]

Dai, J. L.

W. H. Zhang, T. Wu, L. Ye, and J. L. Dai, “Optimal real state cloning in d dimensions,” Phys. Rev. A 75, 044303–044307(2007);
[CrossRef]

Deng, H.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Dieks, D.

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[CrossRef]

Du, J.

T. Durt and J. Du, “Characterization of low-cost one-to-two qubit cloning,” Phys. Rev. A 69, 062316–062326 (2004).
[CrossRef]

Du, J. F.

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317–012322 (2007).
[CrossRef]

Duan, L. M.

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902–127906 (2004).
[CrossRef] [PubMed]

Durt, T.

T. Durt and J. Du, “Characterization of low-cost one-to-two qubit cloning,” Phys. Rev. A 69, 062316–062326 (2004).
[CrossRef]

Dušek, M.

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Felinto, D.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Feng, M.

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A 79, 064304–064308 (2009).
[CrossRef]

Fiurášek, J.

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Gao, J.

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Guo, G. C.

X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
[CrossRef]

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Han, Z. F.

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

Hillery, M.

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef] [PubMed]

Howell, J. C.

A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef] [PubMed]

Karlsson, A.

Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
[CrossRef] [PubMed]

Kimble, H. J.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902–127906 (2004).
[CrossRef] [PubMed]

Lamas-Linares, A.

A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef] [PubMed]

Laurat, J.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Leuchs, G.

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312–052317 (2008).
[CrossRef]

M. Sabuncu, U. L. Andersen, and G. Leuchs, “Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503–170507 (2007).
[CrossRef]

Lin, X. M.

X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
[CrossRef]

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Lu, C. Y.

Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
[CrossRef] [PubMed]

Macchiavello, C.

D. Bruß, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302–012309 (2000).
[CrossRef]

Maunz, P.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Mei, D.

C. S. Yu, X. X. Yi, H. S.Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301–044305 (2007).
[CrossRef]

Pan, J. W.

Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. 95, 030502–030506 (2005).
[CrossRef] [PubMed]

Pinkse, P. W. H.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Puppe, T.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Raimond, J. M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

Rempe, G.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Riedmatten, H. D.

C. W. Chou, J. Laurat, H. Deng, K. S. Choi, H. D. Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320 (2007).
[CrossRef] [PubMed]

Sabuncu, M.

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312–052317 (2008).
[CrossRef]

M. Sabuncu, U. L. Andersen, and G. Leuchs, “Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503–170507 (2007).
[CrossRef]

Schuster, I.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Simon, C.

A. Lamas-Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef] [PubMed]

Song, H. S.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger—Horne—Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127–021130 (2008).
[CrossRef]

C. S. Yu, X. X. Yi, H. S.Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301–044305 (2007).
[CrossRef]

Song, J.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger—Horne—Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127–021130 (2008).
[CrossRef]

Soubusta, J.

J. Soubusta, L. Bartůšková, A. Černoch, M. Dušek, and J. Fiurášek, “Experimental asymmetric phase-covariant quantum cloning of polarization qubits,” Phys. Rev. A 78, 052323–052330(2008).
[CrossRef]

Suter, D.

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317–012322 (2007).
[CrossRef]

Syassen, N.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Normal-mode spectroscopy of a single-bound-atom–cavity system,” Phys. Rev. Lett. 94, 033002–033006 (2005).
[CrossRef] [PubMed]

Wootters, W. K.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[CrossRef]

Wu, T.

W. H. Zhang, T. Wu, L. Ye, and J. L. Dai, “Optimal real state cloning in d dimensions,” Phys. Rev. A 75, 044303–044307(2007);
[CrossRef]

Xia, Y.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger—Horne—Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127–021130 (2008).
[CrossRef]

Xiao, Y. F.

X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
[CrossRef]

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Yang, Y.

Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A 70, 042314–042319 (2004).
[CrossRef]

Ye, L.

W. H. Zhang and L. Ye, “Optimal asymmetric phase-covariant and real state cloning in d dimensions,” New J. Phys. 9, 318–332(2007).
[CrossRef]

W. H. Zhang, T. Wu, L. Ye, and J. L. Dai, “Optimal real state cloning in d dimensions,” Phys. Rev. A 75, 044303–044307(2007);
[CrossRef]

Ye, M. Y.

X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323–012330 (2006).
[CrossRef]

Yi, X. X.

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Figures (3)

Fig. 1
Fig. 1

(a) Representative level diagrams of three trapped atoms. The | 0 | e transition of the atoms is resonant to the | H polarization component of the cavity mode with the coupling constant g. (b) Schematic illustration for the CPF gate between the atom and the photon with a PBS. The | H polarization component of an input single-photon pulse driving the cavity mode is reflected by the cavity while the | V polarization component is reflected by mirror M.

Fig. 2
Fig. 2

Scheme diagram of the quantum-controlled not gate between three distant atoms. HWP1, HWP2, and HWP3 are three half-wave plates. PBS1, PBS2, PBS3, and PBS4 are polarization beam splitters. C1, C2, and C3 are the circulators. M1, M2, and M3 are mirrors. The path of the photon pulse is port–C1–PBS1–cavity 1–PBS1–C1–HWP1–HWP2–C2–PBS2–cavity 2–PBS2–C2–C3–PBS3–cavity 3–PBS3–C3–HWP3–PBS4–D1 (D2). D1 and D2 are single-photon detectors.

Fig. 3
Fig. 3

Schematic illustration for realizing a quantum RSC machine in cavity QED. HWPa, HWPb, and HWPc are half-wave plates. PBSa, PBSb, PBSc, and PBSd are polarization beam splitters. Ca, Cb, and Cc are the circulators. Ma, Mb, and Mc are mirrors. The path of the photon pulse is port–Ca–PBSa–Cavity a–PBSa–Ca–Cb–PBSb–Cavity b–PBSb–Cb–HWPa–HWPb–Cc–PBSc–Cavity c–PBSc–Cc–HWPc–PBSd–Da (Db). Da and Db are single-photon detectors.

Equations (22)

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U CPF = e i π | 1 1 | | H H | .
| ψ s = | ψ 1 | ψ 23 ,
1 2 [ | H ( a | 0 1 b | 1 1 ) + | V ( a | 0 1 + b | 1 1 ) ] | ψ 23 .
( | V a | 0 1 | H b | 1 1 ) | ψ 23 .
| V a | 0 1 | ψ 23 | H b | 1 1 | ψ 23 ,
| V a | 0 1 | ψ 23 | H b | 1 1 | ψ ¯ 23 ,
[ | H ( a | 0 1 | ψ 23 b | 1 1 | ψ ¯ 23 ) | V ( a | 0 1 | ψ 23 + b | 1 1 | ψ ¯ 23 ) ] / 2 .
a | 0 1 | ψ 23 b | 1 1 | ψ ¯ 23 .
a | 0 1 | ψ 23 + b | 1 1 | ψ ¯ 23 ,
a | 0 1 | ψ 23 + b | 1 1 | ψ ¯ 23 .
[ | H ( cos θ 1 | 0 1 sin θ 1 | 1 1 ) + | V ( cos θ 1 | 0 1 + sin θ 1 | 1 1 ) ] / 2 .
[ | H ( cos θ 1 | 0 1 sin θ 1 | 1 1 ) ( cos θ 2 | 0 2 sin θ 2 | 1 2 ) + | V ( cos θ 1 | 0 1 + sin θ 1 | 1 1 ) ( cos θ 2 | 0 2 + sin θ 2 | 1 2 ) ] / 2 .
| V ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | H ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) .
| V ( λ | + 3 + μ | 3 ) ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | H ( λ | 3 + μ | + 3 ) ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) .
| H { λ [ sin φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | + 3 cos φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | 3 ] + μ [ sin φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | 3 cos φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | + 3 ] } | V { λ [ cos φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | + 3 + sin φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | 3 ] + μ [ cos φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | 3 + sin φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | + 3 ] } .
| H { λ [ sin φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | 0 3 cos φ ( cos θ 1 sin θ 2 | 1 1 | 0 2 + sin θ 1 cos θ 2 | 0 1 | 1 2 ) | 1 3 ] + μ [ sin φ ( cos θ 1 cos θ 2 | 1 1 | 1 2 + sin θ 1 sin θ 2 | 0 1 | 0 2 ) | 1 3 cos φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | 0 3 ] } | V { λ [ cos φ ( cos θ 1 cos θ 2 | 0 1 | 0 2 + sin θ 1 sin θ 2 | 1 1 | 1 2 ) | 0 3 + sin φ ( cos θ 1 sin θ 2 | 1 1 | 0 2 + sin θ 1 cos θ 2 | 0 1 | 1 2 ) | 1 3 ] + μ [ cos φ ( cos θ 1 cos θ 2 | 1 1 | 1 2 + sin θ 1 sin θ 2 | 0 1 | 0 2 ) | 1 3 + sin φ ( cos θ 1 sin θ 2 | 0 1 | 1 2 + sin θ 1 cos θ 2 | 1 1 | 0 2 ) | 0 3 ] } .
λ [ ( sin φ cos θ 1 cos θ 2 | 0 3 | 0 2 cos φ sin θ 1 cos θ 2 | 1 3 | 1 2 ) | 0 1 + ( sin φ sin θ 1 sin θ 2 | 0 3 | 1 2 cos φ cos θ 1 sin θ 2 | 1 3 | 0 2 ) | 1 1 ] + μ [ ( sin φ cos θ 1 cos θ 2 | 1 3 | 1 2 cos φ sin θ 1 cos θ 2 | 0 3 | 0 2 ) | 1 1 + ( sin φ sin θ 1 sin θ 2 | 1 3 | 0 2 cos φ cos θ 1 sin θ 2 | 0 3 | 1 2 ) | 0 1 ] .
λ [ ( cos φ cos θ 1 cos θ 2 | 0 3 | 0 2 + sin φ sin θ 1 cos θ 2 | 1 3 | 1 2 ) | 0 1 + sin φ cos θ 1 sin θ 2 | 1 3 | 0 2 + cos φ sin θ 1 sin θ 2 | 0 3 | 1 2 ) | 1 1 ] + μ [ ( cos φ cos θ 1 cos θ 2 | 1 3 | 1 2 + sin φ sin θ 1 cos θ 2 | 0 3 | 0 2 ) | 1 1 + sin φ cos θ 1 sin θ 2 | 0 | 1 2 + cos φ sin θ 1 sin θ 2 | 1 3 | 0 2 ) | 0 1 ] .
ρ 2 = [ λ 2 cos 2 θ 1 ( cos 2 φ sin 2 θ 2 + sin 2 φ cos 2 θ 2 ) + μ 2 sin 2 θ 1 ( cos 2 φ cos 2 θ 2 + sin 2 φ sin 2 θ 2 ) ] | 0 2 0 | + [ μ 2 cos 2 θ 1 ( sin 2 φ cos 2 θ 2 + cos 2 φ sin 2 θ 2 ) + λ 2 sin 2 θ 1 ( sin 2 φ sin 2 θ 2 + cos 2 φ cos 2 θ 2 ) ] | 1 2 1 | 1 2 λ μ sin 2 φ sin 2 θ 2 ( | 0 2 1 | + | 1 2 0 | ) ,
ρ 3 = [ λ 2 sin 2 φ ( sin 2 θ 1 sin 2 θ 2 + cos 2 θ 1 cos 2 θ 2 ) + μ 2 cos 2 φ ( sin 2 θ 1 cos 2 θ 2 + cos 2 θ 1 sin 2 θ 2 ) ] | 0 3 0 | + [ μ 2 sin 2 φ ( sin 2 θ 1 sin 2 θ 2 + cos 2 θ 1 cos 2 θ 2 ) + λ 2 cos 2 φ ( sin 2 θ 1 cos 2 θ 2 + cos 2 θ 1 sin 2 θ 2 ) ] | 1 3 1 | + 1 2 λ μ sin 2 θ 1 sin 2 θ 2 ( | 0 3 1 | + | 1 3 0 | ) .
λ [ ( 1 2 + 1 8 ) | 0 3 | 0 2 | 0 1 + 1 8 ( | 1 3 | 0 2 + | 0 3 | 1 2 ) | 1 1 + ( 1 2 1 8 ) | 1 3 | 1 2 | 0 1 ] + μ [ ( 1 2 + 1 8 ) | 1 3 | 1 2 | 1 1 + 1 8 ( | 0 3 | 1 2 + | 1 3 | 0 2 ) | 0 1 + ( 1 2 1 8 ) | 0 3 | 0 2 | 1 1 ] .
λ [ 3 2 | 0 3 | 0 2 | 0 1 + 1 2 3 ( | 1 3 | 0 2 | 1 1 + | 1 3 | 1 2 | 0 1 + | 0 3 | 1 2 | 1 1 ) ] + μ [ 3 2 | 1 3 | 1 2 | 1 1 + 1 2 3 ( | 0 3 | 1 2 | 0 1 + | 0 3 | 0 2 | 1 1 + | 1 3 | 0 2 | 0 1 ] .

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