Abstract

A method for exploring photon-number entangled states with weak nonlinearities is described. We show that it is possible to create and detect such entanglement at various scales, ranging from microscopic to macroscopic systems. In the present architecture, we suggest that the maximal phase shift induced in the process of interaction between photons is proportional to photon numbers. Also, in the absence of decoherence we analyze maximum error probability and show its feasibility with current technology.

© 2015 Optical Society of America

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  1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
    [Crossref]
  2. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
    [Crossref]
  3. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
    [Crossref] [PubMed]
  4. S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
    [Crossref]
  5. C. Simon and D. Bouwmeester, “Theory of an entanglement laser,” Phys. Rev. Lett. 91, 053601 (2003).
    [Crossref] [PubMed]
  6. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [Crossref]
  7. P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
    [Crossref]
  8. R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
    [Crossref] [PubMed]
  9. S. Y. Lee, J. Park, H. W. Lee, and H. Nha, “Generating arbitrary photon-number entangled states for continuous-variable quantum informatics,” Opt. Express 20, 14221–14233 (2012).
    [Crossref] [PubMed]
  10. A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
    [Crossref]
  11. H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
    [Crossref] [PubMed]
  12. F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
    [Crossref] [PubMed]
  13. M. Fiorentino and R. G. Beausoleil, “Compact sources of polarization-entangled photons,” Opt. Express 16, 20149–20156 (2008).
    [Crossref] [PubMed]
  14. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
    [Crossref]
  15. F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
    [Crossref]
  16. T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
    [Crossref] [PubMed]
  17. P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
    [Crossref]
  18. N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
    [Crossref] [PubMed]
  19. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005).
    [Crossref] [PubMed]
  20. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
    [Crossref]
  21. T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
    [Crossref] [PubMed]
  22. H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [Crossref] [PubMed]
  23. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [Crossref] [PubMed]
  24. N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
    [Crossref]
  25. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [Crossref]
  26. S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
    [Crossref]
  27. Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
    [Crossref]
  28. D. Ding and F. L. Yan, “Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities,” Acta Phys. Sin. 62, 100304 (2013).
  29. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [Crossref]
  30. P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
    [Crossref]
  31. D. Ding, F. L. Yan, and T. Gao, “Preparation of km-photon concatenated Greenberger-Horne-Zeilinger states for observing distinctive quantum effects at macroscopic scales,” J. Opt. Soc. Am. B 30, 3075–3078 (2013).
    [Crossref]
  32. B. T. Kirby and J. D. Franson, “Nonlocal interferometry using macroscopic coherent states and weak nonlinearities,” Phys. Rev. A 87, 053822 (2013).
    [Crossref]
  33. T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.
  34. Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
    [Crossref]
  35. Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
    [Crossref]
  36. D. Ding and F. L. Yan, “Efficient scheme for three-photon Greenberger-Horne-Zeilinger state generation,” Phys. Lett. A 377, 1088–1094 (2013).
    [Crossref]
  37. D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
    [Crossref]
  38. X. H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
    [Crossref] [PubMed]
  39. 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, 2733–2736 (2000).
    [Crossref] [PubMed]
  40. C. W. Gardiner and P. Zoller, Quantum Noise(Springer, Berlin, 2000), pp. 103–104.
  41. J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
    [Crossref]
  42. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [Crossref]
  43. C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
    [Crossref]
  44. B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
    [Crossref]
  45. W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
    [Crossref]
  46. J. Mertz, T. Debuisschert, A. Heidmann, C. Fabre, and E. Giacobino, “Improvements in the observed intensity correlation of optical parametric oscillator twin beams,” Opt. Lett. 16, 1234–1236 (1991).
    [Crossref] [PubMed]
  47. P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
    [Crossref]
  48. A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
    [Crossref]

2015 (3)

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

X. H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
[Crossref] [PubMed]

2014 (5)

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
[Crossref]

J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
[Crossref]

T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
[Crossref] [PubMed]

P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
[Crossref]

2013 (6)

R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
[Crossref] [PubMed]

D. Ding and F. L. Yan, “Efficient scheme for three-photon Greenberger-Horne-Zeilinger state generation,” Phys. Lett. A 377, 1088–1094 (2013).
[Crossref]

C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
[Crossref]

B. T. Kirby and J. D. Franson, “Nonlocal interferometry using macroscopic coherent states and weak nonlinearities,” Phys. Rev. A 87, 053822 (2013).
[Crossref]

D. Ding and F. L. Yan, “Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities,” Acta Phys. Sin. 62, 100304 (2013).

D. Ding, F. L. Yan, and T. Gao, “Preparation of km-photon concatenated Greenberger-Horne-Zeilinger states for observing distinctive quantum effects at macroscopic scales,” J. Opt. Soc. Am. B 30, 3075–3078 (2013).
[Crossref]

2012 (3)

S. Y. Lee, J. Park, H. W. Lee, and H. Nha, “Generating arbitrary photon-number entangled states for continuous-variable quantum informatics,” Opt. Express 20, 14221–14233 (2012).
[Crossref] [PubMed]

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

2011 (2)

F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
[Crossref]

A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
[Crossref]

2010 (1)

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

2009 (3)

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

2008 (3)

F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
[Crossref] [PubMed]

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[Crossref]

M. Fiorentino and R. G. Beausoleil, “Compact sources of polarization-entangled photons,” Opt. Express 16, 20149–20156 (2008).
[Crossref] [PubMed]

2007 (2)

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

2005 (5)

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005).
[Crossref] [PubMed]

2004 (2)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

2003 (1)

C. Simon and D. Bouwmeester, “Theory of an entanglement laser,” Phys. Rev. Lett. 91, 053601 (2003).
[Crossref] [PubMed]

2002 (1)

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

2001 (3)

S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
[Crossref]

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
[Crossref]

2000 (2)

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[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, 2733–2736 (2000).
[Crossref] [PubMed]

1996 (1)

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

1991 (1)

1985 (1)

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref] [PubMed]

Abrams, D. S.

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, 2733–2736 (2000).
[Crossref] [PubMed]

Afzelius, M.

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Barrett, S. D.

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

Beausoleil, R. G.

M. Fiorentino and R. G. Beausoleil, “Compact sources of polarization-entangled photons,” Opt. Express 16, 20149–20156 (2008).
[Crossref] [PubMed]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

Bergou, J. A.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

Boto, A. N.

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, 2733–2736 (2000).
[Crossref] [PubMed]

Bouwmeester, D.

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

C. Simon and D. Bouwmeester, “Theory of an entanglement laser,” Phys. Rev. Lett. 91, 053601 (2003).
[Crossref] [PubMed]

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
[Crossref]

Braunstein, S. L.

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, 2733–2736 (2000).
[Crossref] [PubMed]

Bussières, F.

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Chitambar, E.

F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
[Crossref]

Chuang, I. L.

C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
[Crossref]

Chudzicki, C.

J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
[Crossref]

C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
[Crossref]

De Martini, F.

F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
[Crossref] [PubMed]

Debuisschert, T.

Deng, F. G.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

Ding, D.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
[Crossref]

D. Ding and F. L. Yan, “Efficient scheme for three-photon Greenberger-Horne-Zeilinger state generation,” Phys. Lett. A 377, 1088–1094 (2013).
[Crossref]

D. Ding and F. L. Yan, “Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities,” Acta Phys. Sin. 62, 100304 (2013).

D. Ding, F. L. Yan, and T. Gao, “Preparation of km-photon concatenated Greenberger-Horne-Zeilinger states for observing distinctive quantum effects at macroscopic scales,” J. Opt. Soc. Am. B 30, 3075–3078 (2013).
[Crossref]

Dove, J.

J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
[Crossref]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[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, 2733–2736 (2000).
[Crossref] [PubMed]

Durkin, G. A.

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

Edamatsu, K.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

Eisenberg, H. S.

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

Fabre, C.

Fejer, M. M.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Fiorentino, M.

Franson, J. D.

B. T. Kirby and J. D. Franson, “Nonlocal interferometry using macroscopic coherent states and weak nonlinearities,” Phys. Rev. A 87, 053822 (2013).
[Crossref]

Gao, T.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
[Crossref]

T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
[Crossref] [PubMed]

D. Ding, F. L. Yan, and T. Gao, “Preparation of km-photon concatenated Greenberger-Horne-Zeilinger states for observing distinctive quantum effects at macroscopic scales,” J. Opt. Soc. Am. B 30, 3075–3078 (2013).
[Crossref]

F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
[Crossref]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise(Springer, Berlin, 2000), pp. 103–104.

Ghobadi, R.

R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
[Crossref] [PubMed]

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

Ghose, S.

Giacobino, E.

Gisin, N.

P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
[Crossref]

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Guerreiro, T.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Haus, H. A.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref] [PubMed]

He, B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

He, Y. Q.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

Heidmann, A.

Horodecki, K.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

Horodecki, M.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

Horodecki, P.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

Horodecki, R.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

Howell, J. C.

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
[Crossref]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[Crossref] [PubMed]

Imoto, N.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref] [PubMed]

Kaviani, H.

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

Khoury, G.

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

Kirby, B. T.

B. T. Kirby and J. D. Franson, “Nonlocal interferometry using macroscopic coherent states and weak nonlinearities,” Phys. Rev. A 87, 053822 (2013).
[Crossref]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
[Crossref]

Kok, P.

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A 65, 052104 (2002).
[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, 2733–2736 (2000).
[Crossref] [PubMed]

Kosaka, H.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

Kowalewska-Kudlaszyk, A.

A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
[Crossref]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
[Crossref]

Lamas-Linares, A.

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
[Crossref]

Langrock, C.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Lau, H. W.

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

Lee, H.

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

Lee, H. W.

Lee, S. Y.

Leonski, W.

A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
[Crossref]

Li, X. H.

Lin, Q.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

Long, G. L.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

Lu, C. Y.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

Lvovsky, A.

R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
[Crossref] [PubMed]

Martin, A.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Matsuda, N.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Mertz, J.

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
[Crossref]

Mitsumori, Y.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Nha, H.

Pan, J. W.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Park, J.

Pelc, J. S.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Perina, J.

A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
[Crossref]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Ren, Y. H.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

Rokhsari, H.

Sangouard, N.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
[Crossref]

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Sanguinetti, B.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Schmidt, H.

Sciarrino, F.

F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
[Crossref] [PubMed]

Sekatski, P.

P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
[Crossref]

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Shapiro, J. H.

J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
[Crossref]

C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
[Crossref]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Sheng, Y. B.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Shimizu, R.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

Simon, C.

R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
[Crossref] [PubMed]

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

C. Simon and D. Bouwmeester, “Theory of an entanglement laser,” Phys. Rev. Lett. 91, 053601 (2003).
[Crossref] [PubMed]

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

Spiller, T. P.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

Stobinska, M.

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

Takeuchi, S.

Thew, R. T.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Vahala, K. J.

van Enk, S. J.

T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
[Crossref] [PubMed]

Vitelli, C.

F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
[Crossref] [PubMed]

Wang, J.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Wang, T.

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Williams, C. P.

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, 2733–2736 (2000).
[Crossref] [PubMed]

Xiao, M.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Yamamoto, Y.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref] [PubMed]

Yan, F. L.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
[Crossref]

T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
[Crossref] [PubMed]

D. Ding and F. L. Yan, “Efficient scheme for three-photon Greenberger-Horne-Zeilinger state generation,” Phys. Lett. A 377, 1088–1094 (2013).
[Crossref]

D. Ding and F. L. Yan, “Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities,” Acta Phys. Sin. 62, 100304 (2013).

D. Ding, F. L. Yan, and T. Gao, “Preparation of km-photon concatenated Greenberger-Horne-Zeilinger states for observing distinctive quantum effects at macroscopic scales,” J. Opt. Soc. Am. B 30, 3075–3078 (2013).
[Crossref]

F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
[Crossref]

Yan, S. B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Zbinden, H.

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Zkowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise(Springer, Berlin, 2000), pp. 103–104.

Acta Phys. Sin. (1)

D. Ding and F. L. Yan, “Quantum nondemolition measurement of two-photon Bell-state and three-photon Greenberger-Horne-Zeilinger-state based on weak nonlinearities,” Acta Phys. Sin. 62, 100304 (2013).

J. Opt. B: Quantum Semiclassical Opt. (1)

W. J. Munro, K. Nemoto, T. P. Spiller, S. D. Barrett, P. Kok, and R. G. Beausoleil, “Efficient optical quantum information processing,” J. Opt. B: Quantum Semiclassical Opt. 7, S135–S140 (2005).
[Crossref]

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

J. Phys. B: At. Mol. Opt. Phys. (1)

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Preparation and purification of four-photon Greenberger-Horne-Zeilinger state,” J. Phys. B: At. Mol. Opt. Phys. 48, 055501 (2015).
[Crossref]

Nature (London) (2)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
[Crossref]

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001).
[Crossref]

Nature Photonics (1)

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nature Photonics 3, 95–98 (2009).
[Crossref]

New J. Phys. (2)

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Lett. A (1)

D. Ding and F. L. Yan, “Efficient scheme for three-photon Greenberger-Horne-Zeilinger state generation,” Phys. Lett. A 377, 1088–1094 (2013).
[Crossref]

Phys. Rev. A (14)

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
[Crossref]

B. T. Kirby and J. D. Franson, “Nonlocal interferometry using macroscopic coherent states and weak nonlinearities,” Phys. Rev. A 87, 053822 (2013).
[Crossref]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302 (2005).
[Crossref]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref] [PubMed]

F. L. Yan, T. Gao, and E. Chitambar, “Two local observables are sufficient to characterize maximally entangled states of N qubits,” Phys. Rev. A 83, 022319 (2011).
[Crossref]

P. Sekatski, N. Sangouard, M. Stobińska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states,” Phys. Rev. A 86, 060301 (2012).
[Crossref]

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

A. Kowalewska-Kudłaszyk, W. Leoński, and J. Peřina, “Photon-number entangled states generated in Kerr media with optical parametric pumping,” Phys. Rev. A 83, 052326 (2011).
[Crossref]

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[Crossref]

J. Dove, C. Chudzicki, and J. H. Shapiro, “Phase-noise limitations on single-photon cross-phase modulation with differing group velocities,” Phys. Rev. A 90, 062314 (2014).
[Crossref]

C. Chudzicki, I. L. Chuang, and J. H. Shapiro, “Deterministic and cascadable conditional phase gate for photonic qubits,” Phys. Rev. A 87, 042325 (2013).
[Crossref]

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91, 053832 (2015).
[Crossref]

Phys. Rev. Lett. (11)

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, 2733–2736 (2000).
[Crossref] [PubMed]

R. Ghobadi, A. Lvovsky, and C. Simon, “Creating and detecting micro-macro photon-number entanglement by amplifying and deamplifying a single-photon entangled state,” Phys. Rev. Lett. 110, 170406 (2013).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

C. Simon and D. Bouwmeester, “Theory of an entanglement laser,” Phys. Rev. Lett. 91, 053601 (2003).
[Crossref] [PubMed]

T. Gao, F. L. Yan, and S. J. van Enk, “Permutationally invariant part of a density matrix and nonseparability of N-qubit states,” Phys. Rev. Lett. 112, 180501 (2014).
[Crossref] [PubMed]

P. Sekatski, N. Gisin, and N. Sangouard, “How difficult is it to prove the quantumness of macroscropic states,” Phys. Rev. Lett. 113, 090403 (2014).
[Crossref]

H. S. Eisenberg, G. Khoury, G. A. Durkin, C. Simon, and D. Bouwmeester, “Quantum entanglement of a large number of photons,” Phys. Rev. Lett. 93, 193901 (2004).
[Crossref] [PubMed]

F. De Martini, F. Sciarrino, and C. Vitelli, “Entanglement test on a microscopic-macroscopic system,” Phys. Rev. Lett. 100, 253601 (2008).
[Crossref] [PubMed]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[Crossref] [PubMed]

T. Guerreiro, A. Martin, B. Sanguinetti, J. S. Pelc, C. Langrock, M. M. Fejer, N. Gisin, H. Zbinden, N. Sangouard, and R. T. Thew, “Nonlinear interaction between single photons,” Phys. Rev. Lett. 113, 173601 (2014).
[Crossref] [PubMed]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

Rev. Mod. Phys. (3)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942 (2009).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żkowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Sci. China-Phys. Mech. Astron. (1)

D. Ding, F. L. Yan, and T. Gao, “Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities,” Sci. China-Phys. Mech. Astron. 57, 2098–2103 (2014).
[Crossref]

Other (2)

T. Wang, H. W. Lau, H. Kaviani, R. Ghobadi, and C. Simon, “Strong micro-macro entanglement from a weak cross-Kerr nonlinearity,” arXiv:quant-ph/1412.3090.

C. W. Gardiner and P. Zoller, Quantum Noise(Springer, Berlin, 2000), pp. 103–104.

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Figures (1)

Fig. 1
Fig. 1 The schematic diagram of exploration of photon-number entangled states using weak nonlinearities. Consider n photons traveling through two spatial modes s 1 and s 2 (say signal modes). |α⟩ is a coherent state in probe mode. θ and are phase shifts on the coherent probe beam with several weak cross-Kerr nonlinearities respectively. Rn (θ) is a single phase gate used to evolve coherent state. φm (x) represents a phase shift on one of the signal modes based on the classical feed-forward information.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

| Ψ n : = l = 0 [ n / 2 ] | ψ n l s 1 s 2 = l = 0 [ n / 2 ] ( a l | n l , l s 1 s 2 + b l | l , n l s 1 s 2 ) .
| ψ n l s 1 s 2 = a l | n l , l s 1 s 2 + b l | l , n l s 1 s 2 , l = 0 , 1 , 2 , , [ n / 2 ]
m = 0 n / 2 [ a m | n / 2 + m , n / 2 m s 1 s 2 | α e m ( n 1 ) i θ + b m | n / 2 m , n / 2 + m s 1 s 2 | α e m ( n 1 ) i θ ] .
m = 0 n / 2 f { x , α cos [ m ( n 1 ) θ ] } × ( a m e i ϕ m ( x ) | n / 2 + m , n / 2 m s 1 s 2 + b m e i ϕ m ( x ) | n / 2 m , n / 2 + m s 1 s 2 ) ,
m = 0 ( n 1 ) / 2 [ a m | ( n + 1 ) / 2 + m , ( n 1 ) / 2 m s 1 s 2 | α e 1 2 ( 2 m + 1 ) ( n 1 ) i θ + b m | ( n 1 ) / 2 m , ( n + 1 ) / 2 + m s 1 s 2 | α e 1 2 ( 2 m + 1 ) ( n 1 ) i θ ] .
m = 0 ( n 1 ) / 2 f { x , α cos [ 1 2 ( 2 m + 1 ) ( n 1 ) θ ] } × [ a m e i ϕ ( 2 m + 1 ) / 2 ( x ) | ( n + 1 ) / 2 + m , ( n 1 ) / 2 m s 1 s 2 + b m e i ϕ ( 2 m + 1 ) / 2 ( x ) | ( n 1 ) / 2 m , ( n + 1 ) / 2 + m s 1 s 2 ] ,

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