Abstract

Nonlocal measurement, or instantaneous measurement of nonlocal observables, is a considerably difficult task even for a simple form of product observable, since relativistic causality prohibits interaction between spacelike separate subsystems. Following a recent proposal for effectively creating the von Neumann measurement Hamiltonian of nonlocal observables [Phys. Rev. Lett. 116, 070404 (2016) [CrossRef]  ], here we report a proof-of-principle demonstration of nonlocally measuring a product observable using linear optics without the violation of relativistic causality. Our scheme provides a feasible approach to perform nonlocal measurements via quantum erasure with linear optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. L. Landau and R. Peierls, Z. Phys. 69, 56 (1931).
    [Crossref]
  2. Y. Aharonov and D. Z. Albert, Phys. Rev. D 24, 359 (1981).
    [Crossref]
  3. Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. D 34, 1805 (1986).
    [Crossref]
  4. S. Popescu and L. Vaidman, Phys. Rev. A 49, 4331 (1994).
    [Crossref]
  5. B. Groisman and B. Reznik, Phys. Rev. A 66, 022110 (2002).
    [Crossref]
  6. L. Vaidman, Phys. Rev. Lett. 90, 010402 (2003).
    [Crossref]
  7. S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
    [Crossref]
  8. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
    [Crossref]
  9. C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
    [Crossref]
  10. D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
    [Crossref]
  11. D. Gottesman, "Stabilizer codes and quantum error correction," Thesis (California Institute of Technology, 1997).
  12. K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
    [Crossref]
  13. A. Brodutch and E. Cohen, Phys. Rev. Lett. 116, 070404 (2016).
    [Crossref]
  14. M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982).
    [Crossref]
  15. T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
    [Crossref]
  16. S. Walborn, M. T. Cunha, S. Pádua, and C. Monken, Phys. Rev. A 65, 033818 (2002).
    [Crossref]
  17. A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
    [Crossref]
  18. X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
    [Crossref]
  19. M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
    [Crossref]
  20. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
    [Crossref]
  21. R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 95, 210506 (2005).
    [Crossref]
  22. J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).
    [Crossref]
  23. X.-H. Li, Phys. Rev. A 82, 044304 (2010).
    [Crossref]
  24. Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
    [Crossref]
  25. W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
    [Crossref]

2019 (1)

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

2018 (1)

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

2016 (2)

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
[Crossref]

A. Brodutch and E. Cohen, Phys. Rev. Lett. 116, 070404 (2016).
[Crossref]

2012 (1)

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

2011 (1)

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

2010 (2)

S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
[Crossref]

X.-H. Li, Phys. Rev. A 82, 044304 (2010).
[Crossref]

2006 (1)

Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
[Crossref]

2005 (1)

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

2003 (2)

L. Vaidman, Phys. Rev. Lett. 90, 010402 (2003).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[Crossref]

2002 (2)

S. Walborn, M. T. Cunha, S. Pádua, and C. Monken, Phys. Rev. A 65, 033818 (2002).
[Crossref]

B. Groisman and B. Reznik, Phys. Rev. A 66, 022110 (2002).
[Crossref]

2001 (2)

D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
[Crossref]

J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).
[Crossref]

1999 (1)

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

1995 (1)

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

1994 (1)

S. Popescu and L. Vaidman, Phys. Rev. A 49, 4331 (1994).
[Crossref]

1986 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. D 34, 1805 (1986).
[Crossref]

1982 (1)

M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982).
[Crossref]

1981 (1)

Y. Aharonov and D. Z. Albert, Phys. Rev. D 24, 359 (1981).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

1931 (1)

L. Landau and R. Peierls, Z. Phys. 69, 56 (1931).
[Crossref]

Agnew, M.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. D 34, 1805 (1986).
[Crossref]

Y. Aharonov and D. Z. Albert, Phys. Rev. D 24, 359 (1981).
[Crossref]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. D 34, 1805 (1986).
[Crossref]

Y. Aharonov and D. Z. Albert, Phys. Rev. D 24, 359 (1981).
[Crossref]

Bao, X.-H.

Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
[Crossref]

Beckman, D.

D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
[Crossref]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Boyd, R. W.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[Crossref]

Brodutch, A.

A. Brodutch and E. Cohen, Phys. Rev. Lett. 116, 070404 (2016).
[Crossref]

Brukner, C.

J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).
[Crossref]

Brunner, N.

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

Chen, C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Chen, M.-C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Chen, Z.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Chen, Z.-B.

Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
[Crossref]

Clark, S.

S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
[Crossref]

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Cohen, E.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

A. Brodutch and E. Cohen, Phys. Rev. Lett. 116, 070404 (2016).
[Crossref]

Connor, A.

S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
[Crossref]

Cunha, M. T.

S. Walborn, M. T. Cunha, S. Pádua, and C. Monken, Phys. Rev. A 65, 033818 (2002).
[Crossref]

DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Drevillon, J.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
[Crossref]

Drühl, K.

M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982).
[Crossref]

Ezzahri, Y.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
[Crossref]

Fang, Y.-Q.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Fuchs, C. A.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Gottesman, D.

D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
[Crossref]

D. Gottesman, "Stabilizer codes and quantum error correction," Thesis (California Institute of Technology, 1997).

Groisman, B.

B. Groisman and B. Reznik, Phys. Rev. A 66, 022110 (2002).
[Crossref]

Guo, G.-C.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Han, Y.-J.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Herzog, T. J.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

Hofmann, H. F.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Huang, H.-L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Jaksch, D.

S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
[Crossref]

Jan, M.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Jiang, X.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Joulain, K.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
[Crossref]

Kwiat, P. G.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
[Crossref]

Landau, L.

L. Landau and R. Peierls, Z. Phys. 69, 56 (1931).
[Crossref]

Leach, J.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

Li, C.-F.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Li, L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Li, W.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Li, X.-H.

X.-H. Li, Phys. Rev. A 82, 044304 (2010).
[Crossref]

Liu, C.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Liu, N.-L.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Lu, C.-Y.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Luo, Y.-H.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

McLaren, M.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

Monken, C.

S. Walborn, M. T. Cunha, S. Pádua, and C. Monken, Phys. Rev. A 65, 033818 (2002).
[Crossref]

Mor, T.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Nielsen, M.

D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
[Crossref]

O’Brien, J. L.

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[Crossref]

Okamoto, R.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Ordonez-Miranda, J.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
[Crossref]

Pádua, S.

S. Walborn, M. T. Cunha, S. Pádua, and C. Monken, Phys. Rev. A 65, 033818 (2002).
[Crossref]

Pan, J.-W.

X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 120, 260502 (2018).
[Crossref]

Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
[Crossref]

J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).
[Crossref]

Pan, W.-W.

W.-W. Pan, X.-Y. Xu, E. Cohen, Q.-Q. Wang, Z. Chen, M. Jan, Y.-J. Han, C.-F. Li, and G.-C. Guo, Nanophotonics 8, 1109 (2019).
[Crossref]

Peierls, R.

L. Landau and R. Peierls, Z. Phys. 69, 56 (1931).
[Crossref]

Peruzzo, A.

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

Popescu, S.

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

S. Clark, A. Connor, D. Jaksch, and S. Popescu, New J. Phys. 12, 083034 (2010).
[Crossref]

S. Popescu and L. Vaidman, Phys. Rev. A 49, 4331 (1994).
[Crossref]

Preskill, J.

D. Beckman, D. Gottesman, M. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
[Crossref]

Pryde, G. J.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[Crossref]

Rains, E.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Ralph, T. C.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[Crossref]

Reznik, B.

B. Groisman and B. Reznik, Phys. Rev. A 66, 022110 (2002).
[Crossref]

Roux, F. S.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, Phys. Rev. A 84, 062101 (2011).
[Crossref]

Sasaki, K.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Schmiedmayer, J.

Z.-B. Chen, Q. Zhang, X.-H. Bao, J. Schmiedmayer, and J.-W. Pan, Phys. Rev. A 73, 050302 (2006).
[Crossref]

Scully, M. O.

M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982).
[Crossref]

Shadbolt, P.

A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O’Brien, Science 338, 634 (2012).
[Crossref]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Shor, P. W.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
[Crossref]

Simon, C.

J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature 410, 1067 (2001).
[Crossref]

Smolin, J. A.

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Figures (3)

Fig. 1.
Fig. 1. Scheme for nonlocal measurement of product Pauli observable σzσz. |ψAB and |ψN represent the system state to be measured and an ancillary entangled state, respectively. By using three CNOT gates operated on the system qubits, the ancillary qubits and the local meter qubit, Alice and Bob retain only the measurement results of |0 and |+, respectively, on the ancillary entangled state. Corresponding to the measurement result of local meter qubit, the output state of the observable σzσz is obtained.
Fig. 2.
Fig. 2. Experimental setup for nonlocal measurement. (a) Initial state preparation. An ultrafast laser beam with a central wavelength of 394 nm is focused on a BBO crystal to create photon pairs at 788 nm. Two SPPs and one BS are used to postselect two OAM entangled photons. One HWP and one QWP are placed in sequence at Alice and Bob, respectively, to prepare the initial polarization states. (b) Realization of the Polar-OAM CNOT gate (polarization mode is used as control qubit and OAM mode is used as target qubit) at Alice. (c) Realization of both the Polar-Path CNOT gate (polarization mode is used as a control qubit and path mode is used as a target qubit) and the Polar-OAM CNOT gate at Bob. The measurement of the spatial qubit at (|u+|d)/2 is performed with a prism and a BS while the OAM measurement is performed with SPPs. The tomography of the polarization qubit is then performed with a set of QWP, HWP, and PBS both at Alice and Bob. BBO, beta barium borate; SPP, spiral phase plate; BS, beam splitter; PBS, polarization beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; DP, Dove prism; Comp, optical path compensation.
Fig. 3.
Fig. 3. Reconstructed output density matrix for input state |ϕ4 including real part (left) and imaginary part (right), with the projection to the subspace of Π+ (a) and to the subspace of Π (b), respectively.

Tables (1)

Tables Icon

Table 1. Measurement Results of Fidelity and Probability Projected to the Subspace of Π+ and Π in the Cases of Four Input Statesa