Abstract

We report a novel controllable source of spatial decoherence for twin photons, based upon commercially available wedge depolarizers. This allows us to convert the polarization-entangled singlet state into a tunable mixed state. A full characterization of this mixed state, by means of quantum tomography, shows that such a spatial decoherer can be used for synthesizing Werner-like states on demand.

© 2006 Optical Society of America

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2005

2004

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

2002

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

2001

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

2000

S. Bose and V. Vedral, Phys. Rev. A 61, 040101(R) (2000).
[CrossRef]

1998

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
[CrossRef]

1996

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

1995

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

1994

R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
[CrossRef]

1992

C. H. Bennet, Phys. Rev. Lett. 70, 1895 (1992).
[CrossRef]

1991

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

1989

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef] [PubMed]

Aiello, A.

Altepeter, J. B.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

Barbieri, M.

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

Barraza-Lopez, S.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

Bennet, C. H.

C. H. Bennet, Phys. Rev. Lett. 70, 1895 (1992).
[CrossRef]

Bose, S.

S. Bose and V. Vedral, Phys. Rev. A 61, 040101(R) (2000).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

Branning, D.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000), Chap. 12.

D'Angelo, M.

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

De Martini, F.

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

Di Nepi, G.

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

Ekert, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

Ekert, A. K.

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Gisin, N.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

Guo, G. C.

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

Horodecki, M.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
[CrossRef]

Horodecki, P.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
[CrossRef]

Horodecki, R.

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
[CrossRef]

Huang, Y. F.

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

James, D. F. V.

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Jeffrey, E. R.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

Jozsa, R.

R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
[CrossRef]

Kim, Y. H.

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Kulik, S. P.

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

Kwiat, P. G.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Lee, P. S. K.

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Li, C. F.

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

Mataloni, P.

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Monken, C. H.

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

Munro, W. J.

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000), Chap. 12.

Nogueira, W. A. T.

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

Pádua, S.

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

Peres, A.

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

Peters, N. A.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

Pors, J. B.

Puentes, G.

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Shih, Y.

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

Shih, Y. H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Stefanov, A.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

van Exter, M. P.

Vedral, V.

S. Bose and V. Vedral, Phys. Rev. A 61, 040101(R) (2000).
[CrossRef]

Voigt, D.

Walborn, S. P.

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

Wei, T.-C.

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Werner, R. F.

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef] [PubMed]

White, A. G.

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

Woerdman, J. P.

Wootters, W. K.

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

Zhang, Y. S.

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
[CrossRef]

Nature

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, Nature 409, 1014 (2001).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).
[CrossRef]

S. Bose and V. Vedral, Phys. Rev. A 61, 040101(R) (2000).
[CrossRef]

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef] [PubMed]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, Phys. Rev. A 65, 012301 (2001).
[CrossRef]

Phys. Rev. Lett.

C. H. Bennet, Phys. Rev. Lett. 70, 1895 (1992).
[CrossRef]

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

M. D'Angelo, Y. H. Kim, S. P. Kulik, and Y. Shih, Phys. Rev. Lett. 92, 233601 (2004).
[CrossRef] [PubMed]

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

M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

N. A. Peters, J. B. Altepeter, D. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 92, 133601 (2004).
[CrossRef] [PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

Other

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

A. Aiello and J. P. Woerdman, e-print math-ph/0412061.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000), Chap. 12.

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Figures (3)

Fig. 1
Fig. 1

Experimental scheme: a krypton ion laser pumps a type-II BBO crystal. Walk-off effects are compensated by a half-wave plate and two compensating crystals. The down/converted photons are spatially filtered by single-mode fibers. Additionally, interference filters are placed in both arms for bandwidth selection. A pair of wedge depolarizers in cascade (spatial decoherer) are placed in the idler path. The amount of decoherence can be controlled by varying the azimuthal angle ( α ) between the optical axes (OA1 and OA2) of the two wedges. The decohered twin-photon state is then analyzed by a quantum tomographic procedure by means of polarization analyzers and “bucket” detectors. Bottom box depicts three different settings for α.

Fig. 2
Fig. 2

Real part of the tomographically reconstructed polarization density matrix ρ in the { H , V } basis, as well as calculated tangle T, linear entropy S L , and fidelity F ( ρ t , ρ m ) of the measured state ρ m , with the theoretical target state ρ t for different relative angles ( α ) between the optical axes of the wedges: (a) empty setup (no decoherers), the initial state is the singlet; (b) α = 0 ° antiparallel wedges; (c) α = 15 ° ; and (d) α = 45 ° , the state is a classical statistical mixture.

Fig. 3
Fig. 3

Experimental data for spatial decoherers on the tangle ( T ) -linear entropy ( S L ) plane. Grey area unphysical density matrices. Dashed curve, MEMS; solid curve, Werner states. As the relative angle increases from α = 0 ° to α = 45 ° , the initial singlet state is progressively decohered towards a maximally mixed state. Note that Werner states satisfy T = 0 for S L 8 9 .

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