Abstract

We present two optimal schemes for non-local implementing a single-qubit rotation operation via a maximally entangled quantum channel. We report on the quantitative relations between the quantum action, entangled and classical communication resources required in the implementation. We also put forward two schemes for conclusive implementing the non-local quantum single-qubit rotation via a partially entangled quantum channel. Both these methods can appropriately be referred to as qubit-assisted processes.

© 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 B. Plenio, Phys. Rev. A 62, 052317 (2000).
  13. D. Collins, N. Linden, and S. Popescu, Preprint quan-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. S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).
  17. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
  18. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).
  19. W. Dur, H. J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169 (1999).

2003 (2)

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

J. M. Liu, J. Li, and G. C. Guo, Chin. Opt. Lett. 1, 114 (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 (2)

S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).

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 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)

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

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

1996 (1)

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

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).

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).

Chefles, A.

S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).

Chen, L. B.

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).

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 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).

Huelga, S. F.

S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).

Jacobs, K.

J. Eisert, K. Jacobs, P. Papadopoulos, and 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.

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 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, B.

J. Eisert, K. Jacobs, P. Papadopoulos, and 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).

Schumacher, B.

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

Vaccaro, J. A.

S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).

Vedral, V.

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

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).

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. (1)

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

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

Phys. Lett. A (1)

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

Phys. Rev. A (5)

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

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

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

S. F. Huelga, J. A. Vaccaro, and A. Chefles, Phys. Rev. A 63, 042303 (2001).

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

Phys. Rev. Lett. (3)

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

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

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

Other (2)

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

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

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