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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).

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[CrossRef]

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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[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]

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]
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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]

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[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]

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]

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[CrossRef]
[PubMed]

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[CrossRef]
[PubMed]

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[CrossRef]

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]

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]

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]

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[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]

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

[CrossRef]
[PubMed]

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]

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]

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]

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. 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]

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]

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]

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]

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]

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]

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

[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]

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

[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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]

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]

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, 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]

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]

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. 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]

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

[CrossRef]

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]

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).

[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]

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]

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, 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]
[PubMed]

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]

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]

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. 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]

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]

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]

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]

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]

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]

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]

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]

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]

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[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]
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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).

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[CrossRef]

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]

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]
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[CrossRef]
[PubMed]

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[CrossRef]
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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).

[CrossRef]

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]

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]

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]
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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]

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]

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]
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[CrossRef]
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[CrossRef]
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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]

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[CrossRef]
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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, 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]

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

[CrossRef]

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[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]

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]

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]

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]
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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]
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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]
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[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]
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[CrossRef]

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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).

[CrossRef]
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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).

[CrossRef]
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[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]

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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[CrossRef]
[PubMed]

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[CrossRef]
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[CrossRef]
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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]

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]

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]

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, 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]

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]

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[CrossRef]
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[CrossRef]
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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).

[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]

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]

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]

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]

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]

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]

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]

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[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]

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]

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).

[CrossRef]
[PubMed]

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]

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]
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[CrossRef]
[PubMed]

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[CrossRef]
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[CrossRef]
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[CrossRef]
[PubMed]

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]

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]

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]

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).

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[CrossRef]
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[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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]

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]

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

[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]

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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.

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