Abstract

The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these states must be also of simple manipulation. Spatial qudits states, which are generated by engineering the transverse momentum of the parametric down-converted photons, have been until now considered of hard manipulation. Nevertheless, we show in this work a simple technique for modifying these states. This technique is based on the use of programmable diffractive optical devices, that can act as spatial light modulators, to define the Hilbert space of these photons instead of pre-fabricated multi-slits.

© 2009 Optical Society of America

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    [CrossRef]
  34. G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
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2009

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

W. H. Peeters, J. J. Renema and M. P. van Exter, "Engineering of two-photon spatial quantum correlations behind a double slit," Phys. Rev. A 79043817 (2009).
[CrossRef]

2008

G. Lima F. A. Torres-Ruiz, L. Neves, A Delgado, C Saavedra and S. Padua, "Measurement of spatial qubits," J. Phys. B 41, 185501 (2008).
[CrossRef]

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist and A. G. White, "Manipulating Biphotonic Qutrits," Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

M. T. Gruneisen, W. A. Miller, R. C. Dymale and A. M. Sweiti, "Holographic generation of complex fields with spatial light modulators: Application to quantum key distribution," Appl. Opt. 47, A32-A42 (2008).
[CrossRef] [PubMed]

2007

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

2006

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

E. Yao, S. Franke-Arnold, J. Courtial and M. J. Padgett, "Observation of quantum entanglement using spatial light modulators," Opt. Express 14, 13089-13094 (2006).
[CrossRef] [PubMed]

2005

A. Gogo,W. D. Snyder and M. Beck, "Comparing quantum and classical correlations in a quantum eraser," Phys. Rev. A 71, 052103 (2005).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

2004

R. T. Thew, A. Acın, H. Zbinden and N. Gisin, "Bell-Type Test of Energy-Time Entangled Qutrits," Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
[CrossRef]

J. Plewa, E. Tanner, D. Mueth and D. G. Grier, "Processing carbon nanotubes with holographic optical tweezers," Opt. Express 12, 1978-1981 (2004).
[CrossRef] [PubMed]

2003

D. G. Grier, "A revolution in optical manipulation," Nature 424, 21-27 (2003).
[CrossRef]

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

2002

2001

A. Marquez, C. Iemmi, and I. Moreno "Quantitative predictions of the modulation behavior of twister nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

2000

P. Mogensen and J. Gckstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
[CrossRef]

C. R. Fernandez-Pousa, I. Moreno, N. Bennis and C. Gomez-Reino, "Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays," J. Opt. Soc. Am. A 17, 2074-2080 (2000).
[CrossRef]

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

H. Bechmann-Pasquinucci and A. Peres, "Quantum Cryptography with 3-State Systems," Phys. Rev. A 85, 3313-3316 (2000).

1999

A. Aspect, "Bells inequality test: more ideal than ever," Nature 398, 189-190 (1999).
[CrossRef]

1998

C. H. Monken, P. H. S. Ribeiro and S. Padua, "Transfer of angular spectrum and image formation in spontaneous parametric down-conversion," Phys. Rev. A 57, 3123-3126 (1998).
[CrossRef]

J. A. Davis., I. Moreno, and P. Tsai. "Polarization eigenstates for twisted-nematic liquid-crystal displays," Appl. Opt. 37, 937-945 (1998).
[CrossRef]

1996

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

1994

1966

J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966).
[CrossRef]

Acin, A.

R. T. Thew, A. Acın, H. Zbinden and N. Gisin, "Bell-Type Test of Energy-Time Entangled Qutrits," Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Aguirre Gomez, J. G.

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

Aspect, A.

A. Aspect, "Bells inequality test: more ideal than ever," Nature 398, 189-190 (1999).
[CrossRef]

Baek, S.-Y.

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

Barbosa, G. A.

Barnett, S. M.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and A. Peres, "Quantum Cryptography with 3-State Systems," Phys. Rev. A 85, 3313-3316 (2000).

Beck, M.

A. Gogo,W. D. Snyder and M. Beck, "Comparing quantum and classical correlations in a quantum eraser," Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Bell, J. S.

J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966).
[CrossRef]

Bennis, N.

Bogdanov, Yu. I.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Boyd, R.W.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Buller, G. S.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Campos, J.

Chekhova, M. V.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Chen, J. L.

T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
[CrossRef]

Chiuri, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

Courtial, J.

Coy, J. A.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Davidovich, L.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

Davis, J. A.

De Martini, F.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Delgado, A.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

Dougakiuchi, T.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Durt, T.

T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
[CrossRef]

Dymale, R. C.

Fernandez-Pousa, C. R.

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

C. R. Fernandez-Pousa, I. Moreno, N. Bennis and C. Gomez-Reino, "Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays," J. Opt. Soc. Am. A 17, 2074-2080 (2000).
[CrossRef]

Fonseca, E. J. S.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

Franke-Arnold, S.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

E. Yao, S. Franke-Arnold, J. Courtial and M. J. Padgett, "Observation of quantum entanglement using spatial light modulators," Opt. Express 14, 13089-13094 (2006).
[CrossRef] [PubMed]

Gckstad, J.

Gisin, N.

R. T. Thew, A. Acın, H. Zbinden and N. Gisin, "Bell-Type Test of Energy-Time Entangled Qutrits," Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Gnacinski, P.

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

Gogo, A.

A. Gogo,W. D. Snyder and M. Beck, "Comparing quantum and classical correlations in a quantum eraser," Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Gomez, J. G. A.

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Gomez-Reino, C.

Grier, D. G.

Groblacher, S.

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

Grosz, D. F.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Gruneisen, M. T.

Hofmann, H. F.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Iemmi, C.

A. Marquez, C. Iemmi, and I. Moreno "Quantitative predictions of the modulation behavior of twister nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

Iinuma, M.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Jack, B.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Jennewein, T.

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

Jha, A. K.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Kadoya, Y.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Kasai, K.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Kaszlikowski, D.

T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
[CrossRef]

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

Kim, Y.-H.

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

Kulik, S. P.

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Kwek, L. C.

T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
[CrossRef]

Langford, N. K.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist and A. G. White, "Manipulating Biphotonic Qutrits," Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

Lanyon, B. P.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist and A. G. White, "Manipulating Biphotonic Qutrits," Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

Leach, J.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

Leng, H. Y.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Lima, G.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Marquez, A.

A. Marquez, C. Iemmi, and I. Moreno "Quantitative predictions of the modulation behavior of twister nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

Martinez, O. E.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Maslennikov, G. A.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Mataloni, P.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Miklaszewski, W.

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

Miller, W. A.

Ming, N. B.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Mogensen, P.

Monken, C. H.

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

C. H. Monken, P. H. S. Ribeiro and S. Padua, "Transfer of angular spectrum and image formation in spontaneous parametric down-conversion," Phys. Rev. A 57, 3123-3126 (1998).
[CrossRef]

P. H. S. Ribeiro, C. H. Monken and G. A. Barbosa, "Measurement of coherence area in parametric downconversion luminescence," Appl. Opt. 33, 352-355 (1994).
[CrossRef] [PubMed]

Moreno, I.

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

A. Marquez, C. Iemmi, and I. Moreno "Quantitative predictions of the modulation behavior of twister nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

C. R. Fernandez-Pousa, I. Moreno, N. Bennis and C. Gomez-Reino, "Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays," J. Opt. Soc. Am. A 17, 2074-2080 (2000).
[CrossRef]

Mueth, D.

Neves, L.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Nicolas, J.

Oh, C. H.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Padgett, M. J.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

E. Yao, S. Franke-Arnold, J. Courtial and M. J. Padgett, "Observation of quantum entanglement using spatial light modulators," Opt. Express 14, 13089-13094 (2006).
[CrossRef] [PubMed]

Padua, S.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

C. H. Monken, P. H. S. Ribeiro and S. Padua, "Transfer of angular spectrum and image formation in spontaneous parametric down-conversion," Phys. Rev. A 57, 3123-3126 (1998).
[CrossRef]

Peeters, W. H.

W. H. Peeters, J. J. Renema and M. P. van Exter, "Engineering of two-photon spatial quantum correlations behind a double slit," Phys. Rev. A 79043817 (2009).
[CrossRef]

Peres, A.

H. Bechmann-Pasquinucci and A. Peres, "Quantum Cryptography with 3-State Systems," Phys. Rev. A 85, 3313-3316 (2000).

Plewa, J.

Pomarico, E.

G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
[CrossRef]

Renema, J. J.

W. H. Peeters, J. J. Renema and M. P. van Exter, "Engineering of two-photon spatial quantum correlations behind a double slit," Phys. Rev. A 79043817 (2009).
[CrossRef]

Ribeiro, P. H. S.

C. H. Monken, P. H. S. Ribeiro and S. Padua, "Transfer of angular spectrum and image formation in spontaneous parametric down-conversion," Phys. Rev. A 57, 3123-3126 (1998).
[CrossRef]

P. H. S. Ribeiro, C. H. Monken and G. A. Barbosa, "Measurement of coherence area in parametric downconversion luminescence," Appl. Opt. 33, 352-355 (1994).
[CrossRef] [PubMed]

Rossi, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

Saavedra, C.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Sanchez-Lopez, M. M.

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Santos, I. F.

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

Shurupov, A. P.

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

Snyder, W. D.

A. Gogo,W. D. Snyder and M. Beck, "Comparing quantum and classical correlations in a quantum eraser," Phys. Rev. A 71, 052103 (2005).
[CrossRef]

Straupe, S. S.

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
[CrossRef]

Stutz, M.

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

Sweiti, A. M.

Taguchi, G.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Tanner, E.

Tey, M. K.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Thew, R. T.

R. T. Thew, A. Acın, H. Zbinden and N. Gisin, "Bell-Type Test of Energy-Time Entangled Qutrits," Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Torres-Ruiz, F.A.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

Vallone, G.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
[CrossRef] [PubMed]

G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
[CrossRef]

van Exter, M. P.

W. H. Peeters, J. J. Renema and M. P. van Exter, "Engineering of two-photon spatial quantum correlations behind a double slit," Phys. Rev. A 79043817 (2009).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Velaquez, P.

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

Wang, J. F.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist and A. G. White, "Manipulating Biphotonic Qutrits," Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

Xie, Z. D.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Xu, P.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Yao, E.

A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

E. Yao, S. Franke-Arnold, J. Courtial and M. J. Padgett, "Observation of quantum entanglement using spatial light modulators," Opt. Express 14, 13089-13094 (2006).
[CrossRef] [PubMed]

Yoshimoto, N.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Yu, X. Q.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Yzuel, M. J.

Zaldarriaga, M.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

Zbinden, H.

R. T. Thew, A. Acın, H. Zbinden and N. Gisin, "Bell-Type Test of Energy-Time Entangled Qutrits," Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Zeilinger, A.

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

Zhao, J. S.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Zhu, S. N.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
[CrossRef] [PubMed]

Zhukov, A. A.

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
[CrossRef] [PubMed]

Zukowski, M.

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

M. Stutz, S. Groblacher, T. Jennewein and A. Zeilinger, "How to create and detect N-dimensional entangled photons with an active phase hologram," Appl. Phys. Lett. 90, 261114 (2007).
[CrossRef]

J. Appl. Phys.

I. Moreno, P. Velaquez, C. R. Fernandez-Pousa and M. M. Sanchez-Lopez, "Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display," J. Appl. Phys. 94, 3697-3702 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. B

G. Lima F. A. Torres-Ruiz, L. Neves, A Delgado, C Saavedra and S. Padua, "Measurement of spatial qubits," J. Phys. B 41, 185501 (2008).
[CrossRef]

Nature

D. G. Grier, "A revolution in optical manipulation," Nature 424, 21-27 (2003).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
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Opt. Commun.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, S. Padua, "Generating mixtures of spatial qubits," Opt. Commun. 281, 5058-5906 (2008).
[CrossRef]

Opt. Eng.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, and O. E. Martinez, "Characterization of a liquid crystal television as a programmable spatial light modulator," Opt. Eng. 35, 15-19 (1996).
[CrossRef]

A. Marquez, C. Iemmi, and I. Moreno "Quantitative predictions of the modulation behavior of twister nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann and Y. Kadoya, "Measurement and control of spatial qubits generated by passing photons through double slits," Phys. Rev. A 78, 012307 (2008).
[CrossRef]

G. Lima, L. Neves, I. F. Santos, J. G. Aguirre Gomez, C. Saavedra and S. Padua, "Propagation of spatially entangled qudits through free space," Phys. Rev. A 73, 032340 (2006).
[CrossRef]

A. Gogo,W. D. Snyder and M. Beck, "Comparing quantum and classical correlations in a quantum eraser," Phys. Rev. A 71, 052103 (2005).
[CrossRef]

W. H. Peeters, J. J. Renema and M. P. van Exter, "Engineering of two-photon spatial quantum correlations behind a double slit," Phys. Rev. A 79043817 (2009).
[CrossRef]

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[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich and S. Padua, "Characterizing entanglement in qubits created with spatially correlated twin photons," Phys. Rev. A 76, 032314 (2007).
[CrossRef]

S.-Y. Baek, S. S. Straupe, A. P. Shurupov, S. P. Kulik and Y.-H. Kim, "Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons," Phys. Rev. A 78, 042321 (2008).
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G. Vallone, E. Pomarico, F. De Martini and P. Mataloni, "Experimental realization of polarization qutrits from nonmaximally entangled states," Phys. Rev. A 76, 012319 (2007).
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A. K. Jha, B. Jack, E. Yao, J. Leach, R.W. Boyd, G. S. Buller, S. M. Barnett, S. Franke-Arnold and M. J. Padgett, "Fourier relationship between the angle and angular momentum of entangled photons," Phys. Rev. A 78, 043810 (2008).
[CrossRef]

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T. Durt, D. Kaszlikowski, J. L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Phys. Rev. A 69, 032313 (2004).
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Phys. Rev. Lett.

D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski and A. Zeilinger, "Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000).
[CrossRef] [PubMed]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, J. L. OBrien, K. J. Resch, A. Gilchrist and A. G. White, "Manipulating Biphotonic Qutrits," Phys. Rev. Lett. 100, 060504 (2008).
[CrossRef] [PubMed]

Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh and M. K. Tey, "Qutrit State Engineering with Biphotons," Phys. Rev. Lett. 93, 230503 (2004).
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A. Rossi, G. Vallone, A. Chiuri, F. De Martini and P. Mataloni, "Multipath Entanglement of Two Photons," Phys. Rev. Lett. 102, 153902 (2009).
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L. Neves, G. Lima, J. G. A. Gomez, C. H. Monken, C. Saavedra and S. Padua, "Generation of Entangled States of Qudits using Twin Photons," Phys. Rev. Lett. 94, 100501 (2005).
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X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu and N. B. Ming, "Transforming Spatial Entanglement Using a Domain-Engineering Technique," Phys. Rev. Lett. 101, 233601 (2008).
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Rev. Mod. Phys.

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Other

A. B. Klimov, C. Muoz, A. Fernandez and C. Saavedra, "Optimal quantum-state reconstruction for cold trapped ions," Phys. Rev. A 77, 060303(R) (2008).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup. See the main text for details. In this figure, BBO represents the non-linear crystal used to generate the twin photons. Li and Ls are lenses with focal lengths of 150 mm and 300 mm, respectively, which are placed at the propagation path of the idler and the signal beams, at a distance of 900 mm and 600 mm of the BBO crystal, respectively. P 1 and P 2 are the polarizers which are placed close to a twisted nematic liquid crystal display (LCD) to build our spatial light modulator. The LCD panel is at a distance of 600 mm of the BBO crystal and these polarizers are 2 cm away from the LCD panel. The photo detectors of the idler and signal photons are represented by Di and Ds , respectively. CC is the circuit used to record the coincidence counts between these detectors. The idler photon is detected with the experimental setup in two distinct configurations: At the first one, the detector Di is placed at the LCD plane of image formation which is at 1200 mm from the crystal. At the second one, this detector is moved to the focal plane of Li lens which is at 1050 mm from the crystal. The signal photons are detected at the focal plane of lens Ls which is at 900 mm from the crystal. In (b) a sketch of the four-slit addressed on the LCD and its pixelated structure is shown.

Fig. 2.
Fig. 2.

In (a) it is shown the seven irradiance measurements performed to determine our SLM Jones matrix coefficients. i1n corresponds to an optical configuration where the first and the second polarizers were aligned at the horizontal direction (P 1=P 2=H). For the others curves their directions were: i2n: P 1=H and P 2=V; i3n: P 1=H and P 2=L; i4n: P 1=R and P 2=V; i5n: P 1=45° and P 2=H; i5n: P 1=45° and P 2=V; i7n: P 1=H and P 2=45°, where the indexes H, V, R, L and 45° stand for the horizontal, vertical, right circular, left circular and diagonal polarization directions, respectively. In these curves, the integration time of the data points recorded was 5 s. In (b) we have the values of the Jones matrix coefficients X, Y, Z and W of our SLM. In (c) the predicted and the experimental curves for the transmission of the SLM as a function of its grey level are shown.

Fig. 3.
Fig. 3.

Normalized coincidence counts recorded with detector Di scanning transversally to the image of the SLM-four-slits. The coincidences counts were recorded with a integration time of 5 s. In (a) it is shown the image of the initial four-slit [100, 100, 100, 100]. In (b) we have the image recorded for the modified four-slit [100, 75, 50, 25] and in (c) the image of the four-slit [50, 100, 25, 100]. See the text for details.

Fig. 4.
Fig. 4.

Fig. 4. Interference patterns recorded in coincidence as a function of the detector Di transverse position. In (a) it is shown the interference of the initial four-slit [100, 100, 100, 100]. In (b) it is shown the interference pattern of the modified four-slit [100, 75, 50, 25]. In (c) it is shown the interference pattern of the modified four-slit [50, 100, 25, 100]. See the text for details. The solid lines were obtained theoretically considering the states of Eq. (4), Eq. (5) and Eq. (6), respectively.

Equations (6)

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|ψ=(l=3232αl|li)|γs,
|liaπdqieiqildsinc(qia)|1qi.
M=exp(iϖ)[XiYZiWZiWX+iY],
|ζ1i=12×(|32+|12+|12+|32).
|ζ2i=0.63|32+0.54|12+0.44|12+0.31|32,
ζ3i=0.4232+0.6012+0.3012+0.6032,

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