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]
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    [CrossRef]
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    [CrossRef]
  33. C. R. Fernández-Pousa, I. Moreno, N. Bennis, and C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal non-absorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
    [CrossRef]
  34. G. Lima, L. Neves, I F. Santos, J. G. Aguirre Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
    [CrossRef]
  35. G. Lima, F. A. Torres-Ruiz, L. Neves, A Delgado, C Saavedra, and S. Pádua, “Measurement of spatial qubits,” J. Phys. B 41, 185501 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (2)

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 (9)

G. Lima, F. A. Torres-Ruiz, L. Neves, A Delgado, C Saavedra, and S. Pádua, “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]

A. B. Klimov, C. Muoz, A. Fernández, and C. Saavedra, “Optimal quantum-state reconstruction for cold trapped ions,” Phys. Rev. A 77, 060303(R) (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]

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, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (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]

2007 (3)

M. Stütz, S. Gröblacher, 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. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

2006 (2)

G. Lima, L. Neves, I F. Santos, J. G. Aguirre Gómez, C. Saavedra, and S. Pádua, “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 (2)

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. Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of Entangled States of Qudits using Twin Photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

2004 (4)

R. T. Thew, A. Acín, 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 (2)

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

I. Moreno, P. Veláquez, C. R. Fernández-Pousa, and M. M. Sánchez-López, “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 (1)

2001 (2)

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]

A. Márquez, 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]

2000 (4)

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

C. R. Fernández-Pousa, I. Moreno, N. Bennis, and C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal non-absorbing 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 (1)

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

1998 (2)

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “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 (1)

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 (1)

1966 (1)

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

Acín, A.

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

Aguirre Gómez, J. G.

G. Lima, L. Neves, I F. Santos, J. G. Aguirre Gómez, C. Saavedra, and S. Pádua, “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. Pádua, “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, and S. Pádua, “Measurement of spatial qubits,” J. Phys. B 41, 185501 (2008).
[CrossRef]

Delgado, A.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (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.

Fernández, A.

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

Fernández-Pousa, C. R.

I. Moreno, P. Veláquez, C. R. Fernández-Pousa, and M. M. Sánchez-López, “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. Fernández-Pousa, I. Moreno, N. Bennis, and C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal non-absorbing 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. Pádua, “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.

Gilchrist, A.

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]

Gisin, N.

R. T. Thew, A. Acín, 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]

Gómez, J. G. A.

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

Gómez-Reino, C.

Grier, D. G.

Gröblacher, S.

M. Stütz, S. Gröblacher, 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. Márquez, 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. Stütz, S. Gröblacher, 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]

Klimov, A. B.

A. B. Klimov, C. Muoz, A. Fernández, and C. Saavedra, “Optimal quantum-state reconstruction for cold trapped ions,” Phys. Rev. A 77, 060303(R) (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, and S. Pádua, “Measurement of spatial qubits,” J. Phys. B 41, 185501 (2008).
[CrossRef]

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (2008).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “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 Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “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]

Márquez, A.

A. Márquez, 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. Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “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. Pádua, “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. Veláquez, C. R. Fernández-Pousa, and M. M. Sánchez-López, “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. Márquez, 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. Fernández-Pousa, I. Moreno, N. Bennis, and C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal non-absorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
[CrossRef]

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

Mueth, D.

Muoz, C.

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

Neves, L.

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

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (2008).
[CrossRef]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “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 Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

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

Nicolas, J.

OBrien, J. L.

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]

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]

Pádua, S.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (2008).
[CrossRef]

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

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “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 Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. G. A. Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “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. Pádua, “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]

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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]

Resch, K. 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]

Ribeiro, P. H. S.

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “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, and S. Pádua, “Measurement of spatial qubits,” J. Phys. B 41, 185501 (2008).
[CrossRef]

Saavedra, C.

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

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (2008).
[CrossRef]

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

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

Sánchez-López, M. M.

I. Moreno, P. Veláquez, C. R. Fernández-Pousa, and M. M. Sánchez-López, “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 Gómez, C. Saavedra, and S. Pádua, “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]

Stütz, M.

M. Stütz, S. Gröblacher, 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. Acín, 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, and S. Pádua, “Measurement of spatial qubits,” J. Phys. B 41, 185501 (2008).
[CrossRef]

Torres-Ruiz, F.A.

G. Lima, F.A. Torres-Ruiz, L. Neves, A. Delgado, C. Saavedra, and S. Pádua, “Generating mixtures of spatial qubits,” Opt. Commun. 281, 5058–59062 (2008).
[CrossRef]

Tsai, P.

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]

Veláquez, P.

I. Moreno, P. Veláquez, C. R. Fernández-Pousa, and M. M. Sánchez-López, “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]

White, A. G.

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. Acín, H. Zbinden, and N. Gisin, “Bell-Type Test of Energy-Time Entangled Qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Zeilinger, A.

M. Stütz, S. Gröblacher, 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.

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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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