Abstract

Tremendous progress has been realized in quantum optics for engineering and detecting the quantum properties of light. Today, photon pairs are routinely created in entangled states. Entanglement is revealed using single-photon detectors in which a single photon triggers an avalanche current. The resulting signal is then processed and stored in a computer. Here, we propose an approach to get rid of all the electronic devices between the photons and the experimentalist, i.e., to use the experimentalist’s eye to detect entanglement. We show in particular that the micro-entanglement that is produced by sending a single photon into a beam splitter can be detected with the eye using the magnifying glass of a displacement in phase space. The feasibility study convincingly demonstrates the possibility of realizing the first experiment where entanglement is observed with the eye.

© 2016 Optical Society of America

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References

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    [Crossref]
  2. F. Rieke and D. A. Baylor, Rev. Mod. Phys. 70, 1027 (1998).
    [Crossref]
  3. N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
    [Crossref]
  4. P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
    [Crossref]
  5. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
    [Crossref]
  6. E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
    [Crossref]
  7. N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
    [Crossref]
  8. P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
    [Crossref]
  9. F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
    [Crossref]
  10. M. G. A. Paris, Phys. Lett. A 217, 78 (1996).
    [Crossref]
  11. K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1998).
    [Crossref]
  12. A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
    [Crossref]
  13. B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
    [Crossref]
  14. V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
    [Crossref]
  15. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
    [Crossref]
  16. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
    [Crossref]
  17. N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
    [Crossref]
  18. O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
    [Crossref]
  19. G. A. Barbosa, “Can humans see beyond intensity images,” arXiv:1202.5434 (2012).

2015 (2)

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

2014 (1)

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

2013 (2)

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

2011 (1)

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

2010 (1)

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

2009 (1)

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

2008 (1)

N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
[Crossref]

2004 (1)

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

2000 (1)

A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
[Crossref]

1998 (2)

K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1998).
[Crossref]

F. Rieke and D. A. Baylor, Rev. Mod. Phys. 70, 1027 (1998).
[Crossref]

1996 (3)

M. G. A. Paris, Phys. Lett. A 217, 78 (1996).
[Crossref]

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
[Crossref]

1969 (1)

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

1942 (1)

S. Hecht, S. Shlaer, and M. Pirenne, J. Gen. Physiol. 25, 819 (1942).
[Crossref]

Banaszek, K.

K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1998).
[Crossref]

Bancal, J.-D.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Barbosa, G. A.

G. A. Barbosa, “Can humans see beyond intensity images,” arXiv:1202.5434 (2012).

Baylor, D. A.

F. Rieke and D. A. Baylor, Rev. Mod. Phys. 70, 1027 (1998).
[Crossref]

Bessarab, D. A.

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

Björk, G.

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

Branciard, C.

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
[Crossref]

Brunner, N.

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
[Crossref]

Bruno, N.

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

Caprara Vivoli, V.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

Cheng, M. F.

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

Clauser, J. F.

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

D’Auria, V.

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Gisin, N.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
[Crossref]

Guerreiro, T.

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

Hecht, S.

S. Hecht, S. Shlaer, and M. Pirenne, J. Gen. Physiol. 25, 819 (1942).
[Crossref]

Hessmo, B.

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

Heydari, H.

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

Ho, M.

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[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]

Horodecki, M.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
[Crossref]

Horodecki, P.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
[Crossref]

Horodecki, R.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
[Crossref]

Krivitsky, L. A.

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

Kuzmich, A.

A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
[Crossref]

Laurat, J.

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Lim, C. C. W.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

Mandel, L.

A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
[Crossref]

Martin, A.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

Monteiro, F.

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

Morin, O.

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Paris, M. G. A.

M. G. A. Paris, Phys. Lett. A 217, 78 (1996).
[Crossref]

Peres, A.

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[Crossref]

Phan, N. M.

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

Pirenne, M.

S. Hecht, S. Shlaer, and M. Pirenne, J. Gen. Physiol. 25, 819 (1942).
[Crossref]

Pomarico, E.

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

Rieke, F.

F. Rieke and D. A. Baylor, Rev. Mod. Phys. 70, 1027 (1998).
[Crossref]

Sangouard, N.

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Sanguinetti, B.

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

Sekatski, P.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

Shimony, A.

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

Shlaer, S.

S. Hecht, S. Shlaer, and M. Pirenne, J. Gen. Physiol. 25, 819 (1942).
[Crossref]

Simon, C.

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

Thew, R.

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

Thew, R. T.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

Usachev, P.

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

Walmsley, I. A.

A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
[Crossref]

Wodkiewicz, K.

K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1998).
[Crossref]

Zbinden, H.

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

J. Gen. Physiol. (1)

S. Hecht, S. Shlaer, and M. Pirenne, J. Gen. Physiol. 25, 819 (1942).
[Crossref]

Nat. Phys. (1)

N. Bruno, A. Martin, P. Sekatski, N. Sangouard, R. Thew, and N. Gisin, Nat. Phys. 9, 545 (2013).
[Crossref]

New J. Phys. (2)

V. Caprara Vivoli, P. Sekatski, J.-D. Bancal, C. C. W. Lim, A. Martin, R. T. Thew, H. Zbinden, N. Gisin, and N. Sangouard, New J. Phys. 17023023 (2015).
[Crossref]

E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, New J. Phys. 13, 063031 (2011).
[Crossref]

Phys. Lett. A (2)

M. G. A. Paris, Phys. Lett. A 217, 78 (1996).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 1 (1996).
[Crossref]

Phys. Rev. A (2)

N. Brunner, C. Branciard, and N. Gisin, Phys. Rev. A 78, 052110 (2008).
[Crossref]

P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Phys. Rev. A 82, 053814 (2010).
[Crossref]

Phys. Rev. Lett. (9)

F. Monteiro, V. Caprara Vivoli, T. Guerreiro, A. Martin, J.-D. Bancal, H. Zbinden, R. T. Thew, and N. Sangouard, Phys. Rev. Lett. 114, 170504 (2015).
[Crossref]

N. M. Phan, M. F. Cheng, D. A. Bessarab, and L. A. Krivitsky, Phys. Rev. Lett. 112, 213601 (2014).
[Crossref]

P. Sekatski, N. Brunner, C. Branciard, N. Gisin, and C. Simon, Phys. Rev. Lett. 103, 113601 (2009).
[Crossref]

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

K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 82, 2009 (1998).
[Crossref]

A. Kuzmich, I. A. Walmsley, and L. Mandel, Phys. Rev. Lett. 85, 1349 (2000).
[Crossref]

B. Hessmo, P. Usachev, H. Heydari, and G. Björk, Phys. Rev. Lett. 92, 180401 (2004).
[Crossref]

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[Crossref]

O. Morin, J.-D. Bancal, M. Ho, P. Sekatski, V. D’Auria, N. Gisin, J. Laurat, and N. Sangouard, Phys. Rev. Lett. 110, 130401 (2013).
[Crossref]

Rev. Mod. Phys. (1)

F. Rieke and D. A. Baylor, Rev. Mod. Phys. 70, 1027 (1998).
[Crossref]

Other (1)

G. A. Barbosa, “Can humans see beyond intensity images,” arXiv:1202.5434 (2012).

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (1092 KB)      Supplemental-document

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Figures (3)

Fig. 1.
Fig. 1.

Experimental results (circles) showing the probability of seeing coherent light pulses as a function of the mean photon number (taken from [2]). The black line is a guide for the eye. The dashed red line is the response of a threshold detector with loss (threshold at 7 photons and 8% efficiency). Such a detector can be used to distinguish the states | 0 + 1 and | 0 1 when they are displaced in phase space: the displacement operation not only increases the photon number, but also makes the photon distribution distinguishable. This is shown through the two bumps, which are the photon number distributions of | D ( α ) ( 0 + 1 ) and | D ( α ) ( 0 1 ) for α 100 . The inset is a quarter of the x z plane of the Bloch sphere having the vacuum and single-photon Fock states { | 0 , | 1 } as the north and south poles, respectively. A perfect qubit measurement corresponds to a projection along a vector with unit length (dotted line). The POVM element “no click” of a measurement combining a single-photon detector with 8% efficiency and a displacement operation defines a nonunit vector on the sphere for which the angle with the z axis can be changed by tuning the amplitude of the displacement (purple dashed curve). For a displacement with a zero amplitude (no displacement), this vector points out in the z direction, whereas for an amplitude 12.5 , the vector points out in the x direction. The POVM element “not seen” of a measurement combining a human eye with a displacement operation also defines a nonunit vector on the sphere (blue full line). The angle between this vector and the z axis can also be varied by changing the size of the displacement. In particular, for an amplitude of the displacement of 100 , this vector points out in the x direction, and in this case, the measurement with the eye is fairly similar to the measurement with the single-photon detector with the same efficiency. Rotation in the x y plane can be obtained by changing the phase of the displacement operation.

Fig. 2.
Fig. 2.

Scheme of our proposal for detecting entanglement with the human eye. A photon pair source based on spontaneous parametric down-conversion is used as a single-photon source, the emission of a photon being heralded by the detection of its twin. The heralded photon is then sent into a beam splitter to create path entanglement, i.e., entanglement between two optical modes sharing a delocalized single photon. The entangled state is subsequently detected using a photon counting detector preceded by a displacement operation on one mode and using a human eye preceded by a displacement on the other mode. The displacement operations are performed using a coherent state incident on an unbalanced beam splitter. The correlations between the results (click and no click for the photon detector, seen and not seen for the human eye) allows one to conclude about the presence of entanglement, cf. main text.

Fig. 3.
Fig. 3.

Value of the witness that would be measured in the setup shown in Fig. 2 relative to the value that would be obtained from state with a positive partial transpose Δ W = W W ppt as a function of the beam splitter transmission efficiency T under realistic assumption about efficiencies, cf. main text.

Equations (4)

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| ψ + = 1 2 ( | 0 A | 1 B + | 1 A | 0 B ) .
W = 0 2 π d φ 2 π U φ U φ ( σ α 1 σ β 7 ) U φ U φ ,
W ppt = i , j = 0 1 i j | W | i j p i j + 2 | 10 | W | 01 | p 00 p 11
p 00 P A B ( + 1 + 1 | 0 β 0 , ρ exp ) P B ( + 1 | β 0 , | 1 ) P A ( + 1 | 0 , ρ exp ) P B ( + 1 | β 0 , | 0 ) P B ( + 1 | β 0 , | 1 ) .

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