Abstract

We describe an experimental demonstration of a novel three-photon N00N state generation scheme using a single source of photons based on spontaneous parametric down-conversion (SPDC). The three-photon entangled state is generated when a photon is subtracted from a double pair of photons and detected by a heralding counter. Interference fringes measured with an emulated three-photon detector reveal the three-photon de Broglie wavelength and exhibit visibility > 70% without background subtraction.

© 2009 OSA

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  1. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
    [CrossRef] [PubMed]
  2. P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
    [CrossRef]
  3. Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55(4), 2598–2609 (1997).
    [CrossRef]
  4. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89(21), 213601 (2002).
    [CrossRef] [PubMed]
  5. D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
    [CrossRef] [PubMed]
  6. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
    [CrossRef] [PubMed]
  7. U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
    [CrossRef] [PubMed]
  8. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316(5825), 726–729 (2007).
    [CrossRef] [PubMed]
  9. R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,” N. J. Phys. 10(7), 073033 (2008).
    [CrossRef]
  10. J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
    [CrossRef] [PubMed]
  11. M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
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  12. Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15(21), 14244–14250 (2007).
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  15. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
    [CrossRef] [PubMed]
  16. P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
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  17. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
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  18. L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457(7225), 67–70 (2009).
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  19. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [CrossRef] [PubMed]
  20. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835–4838 (1995).
    [CrossRef] [PubMed]
  21. H. Lee, P. Kok, N. J. Cerf, and J. P. Dowling, “Linear optics and projective measurements alone suffice to create large-photon-number path entanglement,” Phys. Rev. A 65(3), 030101 (2002).
    [CrossRef]
  22. P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65(5), 052104 (2002).
    [CrossRef]
  23. J. Fiurášek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65(5), 053818 (2002).
    [CrossRef]
  24. G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiport,” Phys. Rev. A 68(5), 052315 (2003).
    [CrossRef]
  25. H. F. Hofmann, “Generation of highly nonclassical n-photon polarization states by superbunching at a photon bottleneck,” Phys. Rev. A 70(2), 023812 (2004).
    [CrossRef]
  26. N. M. VanMeter, P. Lougovski, D. B. Uskov, K. Kieling, J. Eisert, and J. P. Dowling, “General linear-optical quantum state generation scheme: applications to maximally path-entangled states,” Phys. Rev. A 76(6), 063808 (2007).
    [CrossRef]
  27. H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99(16), 163604 (2007).
    [CrossRef] [PubMed]
  28. A. E. B. Nielsen and K. Mølmer, “Conditional generation of path-entangled optical |N,0+〉|0,N〉 states,” Phys. Rev. A 75(6), 063803 (2007).
    [CrossRef]
  29. H. F. Hofmann and T. Ono, “High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light,” Phys. Rev. A 76(3), 031806 (2007).
    [CrossRef]
  30. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450(7168), 393–396 (2007).
    [CrossRef] [PubMed]
  31. A. Cho, “A new way to beat the limits on shrinking transistors?” Science 312(5774), 672a (2006).
    [CrossRef]
  32. F. W. Sun, Z. Y. Ou, and G. C. Guo, “Projection measurement of the maximally entangled N-photon state for a demonstration of the N-photon de Broglie wavelength,” Phys. Rev. A 73(2), 023808 (2006).
    [CrossRef]
  33. F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74(3), 033812 (2006).
    [CrossRef]
  34. B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Demonstration of the three-photon de Broglie wavelength by projection measurement,” Phys. Rev. A 77(2), 023815 (2008).
    [CrossRef]
  35. K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
    [CrossRef] [PubMed]
  36. N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in bell-state analysis,” Phys. Rev. Lett. 95(21), 210504 (2005).
    [CrossRef] [PubMed]
  37. N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95(21), 210505 (2005).
    [CrossRef] [PubMed]
  38. R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95(21), 210506 (2005).
    [CrossRef] [PubMed]
  39. These two probabilities are reversed if we apply state projection measurements to |2H, 1V>PBS3 or |1H, 2V>PBS3, which reduces the sensitivity to unwanted superfluous states by a factor of nine.
  40. S. J. Bentley and R. W. Boyd, “Nonlinear optical lithography with ultra-high sub-Rayleigh resolution,” Opt. Express 12(23), 5735–5740 (2004).
    [CrossRef] [PubMed]
  41. The visibility determines the lower bound of the magnitude of the off-diagonal density matrix element, and therefore leads to the lower bound of the fidelity.
  42. M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Shrödinger-cat-like states by means of conditional measurments on a beam splitter,” Phys. Rev. A 55(4), 3184–3194 (1997).
    [CrossRef]

2009 (3)

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[CrossRef]

L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457(7225), 67–70 (2009).
[CrossRef] [PubMed]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
[CrossRef] [PubMed]

2008 (2)

R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,” N. J. Phys. 10(7), 073033 (2008).
[CrossRef]

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Demonstration of the three-photon de Broglie wavelength by projection measurement,” Phys. Rev. A 77(2), 023815 (2008).
[CrossRef]

2007 (8)

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
[CrossRef] [PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316(5825), 726–729 (2007).
[CrossRef] [PubMed]

N. M. VanMeter, P. Lougovski, D. B. Uskov, K. Kieling, J. Eisert, and J. P. Dowling, “General linear-optical quantum state generation scheme: applications to maximally path-entangled states,” Phys. Rev. A 76(6), 063808 (2007).
[CrossRef]

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99(16), 163604 (2007).
[CrossRef] [PubMed]

A. E. B. Nielsen and K. Mølmer, “Conditional generation of path-entangled optical |N,0+〉|0,N〉 states,” Phys. Rev. A 75(6), 063803 (2007).
[CrossRef]

H. F. Hofmann and T. Ono, “High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light,” Phys. Rev. A 76(3), 031806 (2007).
[CrossRef]

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef] [PubMed]

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15(21), 14244–14250 (2007).
[CrossRef] [PubMed]

2006 (3)

A. Cho, “A new way to beat the limits on shrinking transistors?” Science 312(5774), 672a (2006).
[CrossRef]

F. W. Sun, Z. Y. Ou, and G. C. Guo, “Projection measurement of the maximally entangled N-photon state for a demonstration of the N-photon de Broglie wavelength,” Phys. Rev. A 73(2), 023808 (2006).
[CrossRef]

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74(3), 033812 (2006).
[CrossRef]

2005 (4)

H. S. Eisenberg, J. F. Hodelin, G. Khoury, and D. Bouwmeester, “Multiphoton path entanglement by nonlocal bunching,” Phys. Rev. Lett. 94(9), 090502 (2005).
[CrossRef] [PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in bell-state analysis,” Phys. Rev. Lett. 95(21), 210504 (2005).
[CrossRef] [PubMed]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95(21), 210505 (2005).
[CrossRef] [PubMed]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95(21), 210506 (2005).
[CrossRef] [PubMed]

2004 (6)

H. F. Hofmann, “Generation of highly nonclassical n-photon polarization states by superbunching at a photon bottleneck,” Phys. Rev. A 70(2), 023812 (2004).
[CrossRef]

D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[CrossRef] [PubMed]

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[CrossRef] [PubMed]

S. J. Bentley and R. W. Boyd, “Nonlinear optical lithography with ultra-high sub-Rayleigh resolution,” Opt. Express 12(23), 5735–5740 (2004).
[CrossRef] [PubMed]

2003 (1)

G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiport,” Phys. Rev. A 68(5), 052315 (2003).
[CrossRef]

2002 (4)

H. Lee, P. Kok, N. J. Cerf, and J. P. Dowling, “Linear optics and projective measurements alone suffice to create large-photon-number path entanglement,” Phys. Rev. A 65(3), 030101 (2002).
[CrossRef]

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65(5), 052104 (2002).
[CrossRef]

J. Fiurášek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65(5), 053818 (2002).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89(21), 213601 (2002).
[CrossRef] [PubMed]

2001 (2)

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
[CrossRef]

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[CrossRef] [PubMed]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

1997 (2)

Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55(4), 2598–2609 (1997).
[CrossRef]

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Shrödinger-cat-like states by means of conditional measurments on a beam splitter,” Phys. Rev. A 55(4), 3184–3194 (1997).
[CrossRef]

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835–4838 (1995).
[CrossRef] [PubMed]

1990 (1)

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
[CrossRef] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Abrams, D. S.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Adamson, R. B. A.

L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457(7225), 67–70 (2009).
[CrossRef] [PubMed]

Anhut, T.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Shrödinger-cat-like states by means of conditional measurments on a beam splitter,” Phys. Rev. A 55(4), 3184–3194 (1997).
[CrossRef]

Aspelmeyer, M.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[CrossRef] [PubMed]

Banaszek, K.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
[CrossRef] [PubMed]

Barrett, M. D.

D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
[CrossRef] [PubMed]

Bartlett, S. D.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef] [PubMed]

Bentley, S. J.

Berry, D. W.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef] [PubMed]

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835–4838 (1995).
[CrossRef] [PubMed]

Boto, A. N.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Bouwmeester, D.

H. S. Eisenberg, J. F. Hodelin, G. Khoury, and D. Bouwmeester, “Multiphoton path entanglement by nonlocal bunching,” Phys. Rev. Lett. 94(9), 090502 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

Braunstein, S. L.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Britton, J.

D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
[CrossRef] [PubMed]

Cable, H.

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99(16), 163604 (2007).
[CrossRef] [PubMed]

Campos, R. A.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
[CrossRef] [PubMed]

Cerf, N. J.

H. Lee, P. Kok, N. J. Cerf, and J. P. Dowling, “Linear optics and projective measurements alone suffice to create large-photon-number path entanglement,” Phys. Rev. A 65(3), 030101 (2002).
[CrossRef]

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[CrossRef] [PubMed]

Chiaverini, J.

D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
[CrossRef] [PubMed]

Cho, A.

A. Cho, “A new way to beat the limits on shrinking transistors?” Science 312(5774), 672a (2006).
[CrossRef]

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835–4838 (1995).
[CrossRef] [PubMed]

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[CrossRef] [PubMed]

Dakna, M.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Shrödinger-cat-like states by means of conditional measurments on a beam splitter,” Phys. Rev. A 55(4), 3184–3194 (1997).
[CrossRef]

Demkowicz-Dobrzanski, R.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
[CrossRef] [PubMed]

Dorner, U.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
[CrossRef] [PubMed]

Dowling, J. P.

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P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65(5), 052104 (2002).
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P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys. Rev. A 63(6), 063407 (2001).
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A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
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J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
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P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65(5), 052104 (2002).
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H. Lee, P. Kok, N. J. Cerf, and J. P. Dowling, “Linear optics and projective measurements alone suffice to create large-photon-number path entanglement,” Phys. Rev. A 65(3), 030101 (2002).
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F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74(3), 033812 (2006).
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N. M. VanMeter, P. Lougovski, D. B. Uskov, K. Kieling, J. Eisert, and J. P. Dowling, “General linear-optical quantum state generation scheme: applications to maximally path-entangled states,” Phys. Rev. A 76(6), 063808 (2007).
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J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
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J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
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R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,” N. J. Phys. 10(7), 073033 (2008).
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T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316(5825), 726–729 (2007).
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R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95(21), 210506 (2005).
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B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Demonstration of the three-photon de Broglie wavelength by projection measurement,” Phys. Rev. A 77(2), 023815 (2008).
[CrossRef]

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74(3), 033812 (2006).
[CrossRef]

F. W. Sun, Z. Y. Ou, and G. C. Guo, “Projection measurement of the maximally entangled N-photon state for a demonstration of the N-photon de Broglie wavelength,” Phys. Rev. A 73(2), 023808 (2006).
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P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
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J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
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K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
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K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
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K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
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B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef] [PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in bell-state analysis,” Phys. Rev. Lett. 95(21), 210504 (2005).
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J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
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K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98(22), 223601 (2007).
[CrossRef] [PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in bell-state analysis,” Phys. Rev. Lett. 95(21), 210504 (2005).
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J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65(11), 1348–1351 (1990).
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R. Okamoto, H. F. Hofmann, T. Nagata, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers,” N. J. Phys. 10(7), 073033 (2008).
[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316(5825), 726–729 (2007).
[CrossRef] [PubMed]

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15(21), 14244–14250 (2007).
[CrossRef] [PubMed]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95(21), 210506 (2005).
[CrossRef] [PubMed]

Schaetz, T.

D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, “Toward Heisenberg-limited spectroscopy with multiparticle entangled states,” Science 304(5676), 1476–1478 (2004).
[CrossRef] [PubMed]

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N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95(21), 210505 (2005).
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L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457(7225), 67–70 (2009).
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M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
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K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89(21), 213601 (2002).
[CrossRef] [PubMed]

Smith, B. J.

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102(4), 040403 (2009).
[CrossRef] [PubMed]

Stefanov, A.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
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Steinberg, A. M.

L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457(7225), 67–70 (2009).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
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N. J. Phys. (1)

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Phys. Rev. Lett. (13)

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Other (3)

The visibility determines the lower bound of the magnitude of the off-diagonal density matrix element, and therefore leads to the lower bound of the fidelity.

These two probabilities are reversed if we apply state projection measurements to |2H, 1V>PBS3 or |1H, 2V>PBS3, which reduces the sensitivity to unwanted superfluous states by a factor of nine.

B. J. Smith, P. J. Mosley, J. S. Lundeen, and I. Walmsley, “Heralded generation of two-photon NOON states for precision quantum metrology,” in Conference on lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2008), paper QFI5.

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Figures (3)

Fig. 1
Fig. 1

Generation and measurement of three-photon N00N states. PBS: polarizing beam splitter; PPBS: partial PBS; HWP: half-wave plate; QWP: quarter-wave plate; IF: interference filter; SPC: single photon counter; SMF: single-mode fiber; FDC: fiber directional coupler.

Fig. 2
Fig. 2

Preparation of the three-photon N00N state generation scheme: (a) HOM interferometry to match the two optical path lengths: two-fold coincidence counts per 1 s as a function of the time delay between the photons entering PBS2 through the upper and the lower paths. The solid curves are Gaussian least-square fits. (b) Adjustment of the HWP2 angle: four-fold coincidence counts of SPC1~SPC4 per 300 s. The dashed line is a sinusoidal fit.

Fig. 3
Fig. 3

Measurement results of single- and three-photon interference. Data points are coincidence counts per 300 s, and error bars represent standard deviations calculated as (counts)1/2. (a) Single-photon interference: two-fold coincidence counts of SPC1 and SPC2; (b) heralded three-photon interference: four-fold coincidence counts of SPC1~SPC4; (c) unheralded three-photon interference: three-fold coincidence counts of SPC2~SPC4; (d) heralded three-photon interference after subtracting the background coincidences due to the triple-pair generation by SPDC.

Equations (4)

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|ΨHWP1=(18aH†   414aH†   2aV†   2+18aV†   4)|0,
|ΨPPBS=(26aH†   2aV+218e2iφaV†  3)|0,
|ΨHWP2=19(iaH†   3+aV†  3)|0=69i|3H,0V+|0H,3V,
aH|01/2e2iθ(aHiaV)|0,aV|01/2e2iθ(iaHaV)|0,

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