Abstract

Ghost-imaging protocols rely on the properties of correlation in propagation direction and in intensity between two spatially multimode fields. We present a detailed theoretical analysis and the experimental realization and characterization of ghost imaging experiments realized with a source of entangled fields based on parametric downconversion seeded with a single multimode thermal field. Eventually, an application of ghost imaging for secure transmission of images is envisaged.

© 2008 Optical Society of America

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  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429-R3432 (1995).
    [CrossRef]
  2. M. D'Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567-596 (2005), and references therein.
    [CrossRef]
  3. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
    [CrossRef]
  4. Y. Shih, “Quantum imaging,” arXiv:0707.0268 (2007).
  5. A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
    [CrossRef]
  6. E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
    [CrossRef]
  7. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef]
  8. A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef] [PubMed]
  9. D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Two-photon imaging with thermal light,” Opt. Lett. 30, 2354-2356 (2005).
    [CrossRef]
  10. O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
    [CrossRef]
  11. M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
    [CrossRef]
  12. M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
    [CrossRef]
  13. H. Cramer, Mathematical Methods of Statistics (Princeton U. Press, 1946).
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    [CrossRef]
  16. C. H. Bennett, “Quantum information and computation,” Phys. Today 48, 24-30 (1995).
    [CrossRef]
  17. D. P. DiVincenzo, “Quantum computation,” Science 270, 255-261 (1995).
    [CrossRef]
  18. A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413-1415 (1996).
    [CrossRef]
  19. P. Horodecki, “Separability criterion and inseparable mixed states with positive partial transposition,” Phys. Lett. A 232, 333-339 (1997).
    [CrossRef]
  20. R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726-2729 (2000).
    [CrossRef]
  21. A. Ferraro, S. Olivares, and M., G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).
  22. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
    [CrossRef]
  23. A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
    [CrossRef]
  24. J. W. Goodman, Fourier Optics (McGraw-Hill, 1968).
  25. E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
    [CrossRef]
  26. I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
    [CrossRef]
  27. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19, 1174-1184 (2002).
    [CrossRef]
  28. A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
    [CrossRef]
  29. F. Paleari, A. Andreoni, G. Zambra, and M. Bondani, “Thermal photon statistics in spontaneous parametric downconversion,” Opt. Express 12, 2816-2824 (2004).
    [CrossRef] [PubMed]
  30. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  31. A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
    [CrossRef]
  32. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]

2007 (5)

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
[CrossRef]

E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
[CrossRef]

2006 (2)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

2005 (4)

D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Two-photon imaging with thermal light,” Opt. Lett. 30, 2354-2356 (2005).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

M. D'Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567-596 (2005), and references therein.
[CrossRef]

2004 (4)

A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

F. Paleari, A. Andreoni, G. Zambra, and M. Bondani, “Thermal photon statistics in spontaneous parametric downconversion,” Opt. Express 12, 2816-2824 (2004).
[CrossRef] [PubMed]

2002 (4)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19, 1174-1184 (2002).
[CrossRef]

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[CrossRef]

2000 (1)

R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726-2729 (2000).
[CrossRef]

1997 (1)

P. Horodecki, “Separability criterion and inseparable mixed states with positive partial transposition,” Phys. Lett. A 232, 333-339 (1997).
[CrossRef]

1996 (1)

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413-1415 (1996).
[CrossRef]

1995 (3)

C. H. Bennett, “Quantum information and computation,” Phys. Today 48, 24-30 (1995).
[CrossRef]

D. P. DiVincenzo, “Quantum computation,” Science 270, 255-261 (1995).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429-R3432 (1995).
[CrossRef]

1985 (1)

D. R. Truax, “Baker-Campbell-Hausdorff relations and unitarity of SU (2) and SU (1,1) squeeze operators,” Phys. Rev. D 31, 1988-1991 (1985).
[CrossRef]

Abouraddy, A. F.

Allevi, A.

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

Andreoni, A.

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
[CrossRef]

E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

F. Paleari, A. Andreoni, G. Zambra, and M. Bondani, “Thermal photon statistics in spontaneous parametric downconversion,” Opt. Express 12, 2816-2824 (2004).
[CrossRef] [PubMed]

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Bennett, C. H.

C. H. Bennett, “Quantum information and computation,” Phys. Today 48, 24-30 (1995).
[CrossRef]

Bondani, M.

A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
[CrossRef]

E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
[CrossRef]

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

F. Paleari, A. Andreoni, G. Zambra, and M. Bondani, “Thermal photon statistics in spontaneous parametric downconversion,” Opt. Express 12, 2816-2824 (2004).
[CrossRef] [PubMed]

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Castelletto, S.

Chen, X. H.

Cramer, H.

H. Cramer, Mathematical Methods of Statistics (Princeton U. Press, 1946).

D'Angelo, M.

M. D'Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567-596 (2005), and references therein.
[CrossRef]

A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

De Siena, S.

A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Degiovanni, I. P.

E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
[CrossRef]

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

Di Trapani, P.

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

DiVincenzo, D. P.

D. P. DiVincenzo, “Quantum computation,” Science 270, 255-261 (1995).
[CrossRef]

Fabre, C.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

Ferraro, A.

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

A. Ferraro, S. Olivares, and M., G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

Ferri, F.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Gatti, A.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Fourier Optics (McGraw-Hill, 1968).

Horodecki, P.

P. Horodecki, “Separability criterion and inseparable mixed states with positive partial transposition,” Phys. Lett. A 232, 333-339 (1997).
[CrossRef]

Illuminati, F.

A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Jedrkiewicz, O.

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

Lugiato, L. A.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Magatti, D.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Olivares, S.

A. Ferraro, S. Olivares, and M., G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

Paleari, F.

Paris, M. G. A.

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 98, 039301 (2007).
[CrossRef]

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

A. Ferraro, S. Olivares, and M., G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, 2005).

Peres, A.

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413-1415 (1996).
[CrossRef]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429-R3432 (1995).
[CrossRef]

Puddu, E.

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

E. Puddu, A. Andreoni, I. P. Degiovanni, M. Bondani, and S. Castelletto, “Ghost imaging with intense fields from chaotically seeded parametric downconversion,” Opt. Lett. 32, 1132-1134 (2007).
[CrossRef]

A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Saleh, B. E. A.

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

Serafini, A.

A. Serafini, F. Illuminati, M., G. A. Paris, and S. De Siena, “Entanglement and purity of two-mode Gaussian states in noisy channels,” Phys. Rev. A 69, 022318 (2004).
[CrossRef]

Sergienko, A. V.

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[CrossRef]

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Y. Shih, “Quantum imaging,” arXiv:0707.0268 (2007).

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M. D'Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567-596 (2005), and references therein.
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429-R3432 (1995).
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R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726-2729 (2000).
[CrossRef]

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T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429-R3432 (1995).
[CrossRef]

Teich, M. C.

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

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D. R. Truax, “Baker-Campbell-Hausdorff relations and unitarity of SU (2) and SU (1,1) squeeze operators,” Phys. Rev. D 31, 1988-1991 (1985).
[CrossRef]

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A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

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G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
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L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

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M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
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[CrossRef] [PubMed]

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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

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Zhang, D.

J. Mod. Opt. (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739-760 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Phys. (1)

A. Allevi, M. Bondani, A. Ferraro, and M. G. A. Paris, “Classical quantum aspects of multimode parametric interactions,” Laser Phys. 16, 1451-1477 (2006).
[CrossRef]

Laser Phys. Lett. (1)

M. D'Angelo and Y. H. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567-596 (2005), and references therein.
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Spectrosc. (1)

A. Andreoni, E. Puddu, and M. Bondani, “Manipulations of chaotic and ghost images for non-local information retrieval,” Opt. Spectrosc. 103, 57-61 (2007).
[CrossRef]

Phys. Lett. A (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

I. P. Degiovanni, M. Bondani, E. Puddu, A. Andreoni, and M. G. A. Paris, “Intensity correlations, entanglement properties, and ghost imaging in multimode thermal-seeded parametric downconversion: Theory,” Phys. Rev. A 76, 062309 (2007).
[CrossRef]

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[CrossRef]

M. Bondani, A. Allevi, G. Zambra, M. G. A. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phys. Rev. A 76, 013833 (2007).
[CrossRef]

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[CrossRef]

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O. Jedrkiewicz, Y.-K. Yang, E. Brambilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di Trapani, “Single-shot detection of spatial quantum correlation in high-gain parametric down-conversion,” Phys. Rev. Lett. 93, 243601 (2004).
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[CrossRef]

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[CrossRef]

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[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost imaging and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D'Angelo, and Y. Shih, “Imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

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[CrossRef]

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http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html.

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Y. Shih, “Quantum imaging,” arXiv:0707.0268 (2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup used for the theoretical description and realization of the ghost-imaging experiment. NLC, nonlinear crystal; L, lens of focal length f; d 1 , d 2 , and q are such that 1 ( d 1 + d 2 ) + 1 q = 1 f (thin lens equation).

Fig. 2
Fig. 2

Plot of the logarithmic negativity E N ( ρ ̂ q , o u t ) as a function of n PDC , q and n t h , q 0 .

Fig. 3
Fig. 3

( a ) Typical single-shot speckle pattern at the entrance face of the crystal; ( b ) the sections of the autocorrelation functions for the speckle pattern in ( a ) injected into the BBO crystal in the R arm (solid curve) and after the interaction at the output of the crystal in the R (dashed curve) and T (dotted curve) arms.

Fig. 4
Fig. 4

Typical single-shot speckle pattern at the object-plane x T , in ( a ) and at the reference plane x R in ( b ) . ( c ) Sections of the autocorrelation functions for the above speckle patterns in the R (red) and T (black) arms. According to Fig. 1, injection is on the R arm.

Fig. 5
Fig. 5

( a ) Statistical distribution of the intensity on the bucket detector (bars) and multithermal fit giving μ T = 35 (solid curve); ( b ) statistical distribution of the intensity in a single pixel of the D R detector (bars) and multithermal fit giving μ R = 1 (solid curve).

Fig. 6
Fig. 6

( a ) Ghost image reconstructed by using 10,000 single-shot maps; ( b ) average of the map pixels in ( a ) along the slit length evaluated according to Eq. (36).

Fig. 7
Fig. 7

( a ) Mean values C N , i n t ( x R ) as a function of N in four selected points of the average of the map pixels displayed in Fig. 6b; ( b ) square root of the variances σ [ C N , i n t ( x R ) ] = σ 2 [ C N , i n t ( x R ) ] as a function of N at the same points of ( a ) .

Fig. 8
Fig. 8

Scheme of an efficient encryption of the image of an object by distributed imaging.

Equations (43)

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i H ̂ I d t = i ( q κ q a ̂ T , q a ̂ R , q + H.c. ) .
S ̂ = q e i O ̂ q .
ρ ̂ R = q ρ ̂ R , q = q { m = 0 p R , q ( m ) m m R , q } ,
ρ ̂ out = S ̂ ( ρ ̂ R 0 0 T ) S ̂ = q [ e i O ̂ q ( ρ ̂ R , q 0 0 T , q ) e i O ̂ q ] ,
e i O ̂ q ( ρ ̂ R , q 0 0 T , q ) e i O ̂ q = m = 0 p T , q ( m ) e i O ̂ q ( m m R , q 0 0 T , q ) e i O ̂ q .
ρ ̂ o u t = q ρ ̂ q , o u t = q n p R , q ( n ) n 1 , n 2 F q ( n , n 1 , n 2 ) n + n 1 n + n 2 R , q n 1 n 2 T , q ,
F q ( n , n 1 , n 2 ) = ( n PDC , q ) n 1 + n 2 2 ( 1 + n PDC , q ) n + 1 + ( n 1 + n 2 ) 2 ( n + n 1 ) ! n ! n 1 ! ( n + n 2 ) ! n ! n 2 ! ,
ρ ̂ o u t , R = Tr T [ ρ ̂ o u t ] = q m = 0 ( n PDC , q + n t h , q + n PDC , q n t h , q ) m ( 1 + n PDC , q + n t h , q + n PDC , q n t h , q ) m + 1 m m R , q ,
ρ ̂ o u t , T = Tr R [ ρ ̂ o u t ] = q m = 0 ( n PDC , q + n PDC , q n t h , q ) m ( 1 + n PDC , q + n PDC , q n t h , q ) m + 1 m m T , q .
X ̂ j , q = a ̂ j , q + a ̂ j , q 2 ,
Y ̂ j , q = a ̂ j , q a ̂ j , q i 2 ( j = R , T ) ,
[ ξ ̂ q , α , ξ ̂ q , β ] = i δ q , q Ω α , β ,
J = ( 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 ) .
V + i 2 Ω 0 ,
b ̂ i , q = e i O ̂ q a ̂ i , q e i O ̂ q = U q a ̂ i , q + e i φ q V q a ̂ j , q ( i , j = R , T , i j ) ,
S ̂ X ̂ i , q S ̂ = e i O ̂ q X ̂ i , q e i O ̂ q = U q X ̂ i , q + V q X ̂ j , q ,
S ̂ Y ̂ i , q S ̂ = e i O ̂ q Y ̂ i , q e i O ̂ q = U q Y ̂ i , q V q Y ̂ j , q ( i , j = R , T , i j ) ,
V = q V q
V q = [ A q 0 C q 0 0 A q 0 C q C q 0 B q 0 0 C q 0 B q ] .
A q = { Δ X ̂ T , q , Δ X ̂ T , q } = { Δ Y ̂ T , q , Δ Y ̂ T , q } = [ U q 2 ( 2 n t h , q + 1 ) + V q 2 ] 2 ,
B q = { Δ X ̂ R , q , Δ X ̂ R , q } = { Δ Y ̂ R , q , Δ Y ̂ R , q } = [ U q 2 + V q 2 ( 2 n t h , q + 1 ) ] 2 ,
C q = { Δ X ̂ T , q , Δ X ̂ R , q } = { Δ Y ̂ T , q , Δ Y ̂ R , q } = = U q V q ( n t h , q + 1 ) .
V ̃ + i 2 Ω 0 ,
n PDC , q ( 1 + n t h , q 0 ) 0 ,
E N ( ρ ̂ q , o u t ) = max { 0 , ln ( 2 d ̃ q , ) } ,
d ̃ q , = A q 2 + B q 2 + 2 C q 2 ( A q + B q ) 2 [ ( A q B q ) 2 4 C q 2 ] .
G ( 2 ) ( x R ) = d x T G ( 2 ) ( x R , x T ) , = d x T { Tr [ Δ I ̂ R ( x R ) Δ I ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] } , = Tr [ I ̂ R ( x R ) I ̂ T ( ρ ̂ R 0 0 T ) ] Tr [ I ̂ R ( x R ) ( ρ ̂ R 0 0 T ) ] Tr [ I ̂ T ( ρ ̂ R 0 0 T ) ] ,
g ( 2 ) ( x R ) = G ( 2 ) ( x R ) Tr [ ( Δ I ̂ R ( x R ) ) 2 ( ρ ̂ R 0 0 T ) ] Tr [ ( Δ I ̂ T ) 2 ( ρ ̂ R 0 0 T ) ] ,
c ̂ i ( x i ) = d x i h i ( x i , x i ) b ̂ i ( x i ) ,
h T ( x T , x T ) = d x h Im ( x T , x ) t ( x ) h F ( d 1 ) ( x , x T ) ,
h R ( x R , x R ) = d x h F ( d 2 ) ( x , x R ) h T ( f ) ( x ) h F ( q ) ( x R , x ) ,
G ( 2 ) ( x R , x T ) = d x R d x R d x T d x T h R ( x R , x R ) h R * ( x R , x R ) h T ( x T , x T ) h T * ( x T , x T ) × { Tr [ b ̂ R ( x R ) b ̂ R ( x R ) b ̂ T ( x T ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] Tr [ b ̂ R ( x R ) b ̂ R ( x R ) ( ρ ̂ R 0 0 T ) ] Tr [ b ̂ T ( x T ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] } .
Tr [ b ̂ R ( x R ) b ̂ R ( x R ) b ̂ T ( x T ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] = Tr [ b ̂ R ( x R ) b ̂ R ( x R ) b ̂ T ( x T ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] + Tr [ b ̂ R ( x R ) b ̂ T ( x T ) b ̂ R ( x R ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] .
G ( 2 ) ( x R , x T ) = d x R d x T h R ( x R , x R ) h T ( x T , x T ) Tr [ b ̂ R ( x R ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] 2 ,
Tr [ b ̂ R ( x R ) b ̂ T ( x T ) ( ρ ̂ R 0 0 T ) ] q e i q ( x T x R ) U q e i φ q V q ( 1 + n t h , q ) .
G ( 2 ) ( x R ) t ( x R M ) 2 d x T q δ ( q 2 π x T λ f ) e i φ q U q V q ( 1 + n t h , q ) 2 t ( x R M ) 2 d x T n PDC ( 2 π x T λ f ) × [ 1 + n PDC ( 2 π x T λ f ) ] [ 1 + n t h ( 2 π x T λ f ) ] 2 .
( slit area ) ( speckle area ) = ( 0.25 mm 2 ) ( π ( 114 2 ) 2 μ m 2 ) 25 .
P μ ( I ) = e μ I I ( I μ ) μ I μ 1 ( μ 1 ) ! ,
C N ( x R ) = N i = 1 N I R , i ( x R ) I T , i i = 1 N I R , i ( x R ) j = 1 N I T , j [ N i = 1 N I R , i ( x R ) 2 ( i = 1 N I R , i ( x R ) ) 2 ] [ N i = 1 N I T , i 2 ( i = 1 N I T , i ) 2 ] .
( C N ( x R ) ± 1 N 1 ) .
C N , i n t ( x R ) = y R C N ( x R , y R ) .
Max [ C N ( x R ) ] K < 3 N 1 ,
9 K 2 S Max [ C N ( x R ) ] 2 log 2 K < M p .

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