Abstract

We show how a non-local quantum controlled-NOT (CNOT) gate with multiple targets can be implemented with unit fidelity and unit probability. The explicit quantum circuit for implementing the operation is presented. Two schemes for probabilistic implementing the operation via partially entangled quantum channels with unit fidelity are put forward. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different.

© 2005 Chinese Optics Letters

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  1. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
  2. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).
  3. J. M. Liu, J. Li, and G. C. Guo, Chin. Opt. Lett. 1, 114 (2003).
  4. H. Lu, Chin. Phys. Lett. 18, 1004 (2001).
  5. H. Lu and G. C. Guo, Phys. Lett. A 276, 209 (2000).
  6. X. Lin and H. C. Li, Acta Opt. Sin. (in Chinese) 23, 137 (2003).
  7. L. B. Chen, Chin. Phys. 11, 999 (2002).
  8. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
  9. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
  10. S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).
  11. D. Gottesman and I. L. Chuang, Nature 402, 390 (1999).
  12. J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).
  13. D. Collins, N. Linden, and S. Popescu, Preprint quant-ph/0005102 (2000).
  14. Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).
  15. L. B. Chen, Chin. Phys. 11, 881 (2002).
  16. L. B. Chen and H. Lu, Chin. Opt. Lett. 2, 59 (2004).
  17. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
  18. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
  19. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).
  20. W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

2004 (1)

2003 (2)

J. M. Liu, J. Li, and G. C. Guo, Chin. Opt. Lett. 1, 114 (2003).

X. Lin and H. C. Li, Acta Opt. Sin. (in Chinese) 23, 137 (2003).

2002 (3)

L. B. Chen, Chin. Phys. 11, 999 (2002).

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

L. B. Chen, Chin. Phys. 11, 881 (2002).

2001 (1)

H. Lu, Chin. Phys. Lett. 18, 1004 (2001).

2000 (2)

H. Lu and G. C. Guo, Phys. Lett. A 276, 209 (2000).

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

1999 (2)

D. Gottesman and I. L. Chuang, Nature 402, 390 (1999).

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

1998 (2)

S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

1997 (2)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

1996 (1)

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

1993 (1)

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

Bose, S.

S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Briegel, H. J.

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

Chen, L. B.

L. B. Chen and H. Lu, Chin. Opt. Lett. 2, 59 (2004).

L. B. Chen, Chin. Phys. 11, 881 (2002).

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

L. B. Chen, Chin. Phys. 11, 999 (2002).

Chuang, I. L.

D. Gottesman and I. L. Chuang, Nature 402, 390 (1999).

Cirac, J. I.

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Dur, W.

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

Eisert, J.

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

Gottesman, D.

D. Gottesman and I. L. Chuang, Nature 402, 390 (1999).

Gu, Y. J.

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

Guo, G. C.

J. M. Liu, J. Li, and G. C. Guo, Chin. Opt. Lett. 1, 114 (2003).

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

H. Lu and G. C. Guo, Phys. Lett. A 276, 209 (2000).

Jacobs, K.

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Kimble, H. J.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

Knight, P. L.

S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).

Li, H. C.

X. Lin and H. C. Li, Acta Opt. Sin. (in Chinese) 23, 137 (2003).

Li, J.

Lin, X.

X. Lin and H. C. Li, Acta Opt. Sin. (in Chinese) 23, 137 (2003).

Liu, J. M.

Lu, H.

L. B. Chen and H. Lu, Chin. Opt. Lett. 2, 59 (2004).

H. Lu, Chin. Phys. Lett. 18, 1004 (2001).

H. Lu and G. C. Guo, Phys. Lett. A 276, 209 (2000).

Mabuchi, H.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

Pan, J. W.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

Papadopoulos, P.

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Plenio, M. B.

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

Popescu, S.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

Reck, M.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

Schumacher, B.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

Vedral, V.

S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).

Weinfuter, H.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

Zeilinger, A.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

Zheng, Y. Z.

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

Zoller, P.

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

Acta Opt. Sin. (in Chinese) (1)

X. Lin and H. C. Li, Acta Opt. Sin. (in Chinese) 23, 137 (2003).

Chin. Opt. Lett. (2)

Chin. Phys. (3)

Y. Z. Zheng, Y. J. Gu, L. B. Chen, and G. C. Guo, Chin. Phys. 11, 529 (2002).

L. B. Chen, Chin. Phys. 11, 881 (2002).

L. B. Chen, Chin. Phys. 11, 999 (2002).

Chin. Phys. Lett. (1)

H. Lu, Chin. Phys. Lett. 18, 1004 (2001).

Nature (2)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfuter, and A. Zeilinger, Nature 390, 575 (1997).

D. Gottesman and I. L. Chuang, Nature 402, 390 (1999).

Phys. Lett. A (1)

H. Lu and G. C. Guo, Phys. Lett. A 276, 209 (2000).

Phys. Rev. A (3)

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317 (2000).

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).

W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

Phys. Rev. A. (1)

S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A. 57, 822 (1998).

Phys. Rev. Lett. (4)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).

Other (2)

D. Collins, N. Linden, and S. Popescu, Preprint quant-ph/0005102 (2000).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

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