Abstract

Coherently manipulating a number of entangled qubits is the key task of quantum information processing. In this paper, we report on the experimental realization of a ten-photon Greenberger–Horne–Zeilinger state using thin BiB3O6 crystals. The observed fidelity is 0.606±0.029, demonstrating a genuine entanglement with a standard deviation of 3.6σ. This result is further verified using p-value calculation, obtaining an upper bound of 3.7×103 under an assumed hypothesis test. Our experiment paves a new way to efficiently engineer BiB3O6 crystal-based multi-photon entanglement systems, which provides a promising platform for investigating advanced optical quantum information processing tasks such as boson sampling, quantum error correction, and quantum-enhanced measurement.

© 2017 Optical Society of America

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  36. The twofold coincidence counting rate of entangled-photon pairs, also known as the brightness of entangled-photon pairs, can be described as RTξ2, while entanglement decays with ∼O(1/RT).
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  38. The spatial walk-offs result in the decay of beam quality, reducing the SPDC photons’ collection efficiency.
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    [Crossref]
  40. Periodically poled KTiOPO4 (ppKTP) can also meet the two requirements. However, the strong frequency correlation in our interested wavelength range prevents ppKTP from being an appropriate candidate for the demonstration of multi-photon entanglement.
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    [Crossref]
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    [Crossref]
  43. Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
    [Crossref]
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    [Crossref]
  45. The two birefringent compensators make the SPDC photons overlap in spatio-temporal mode. However, the distortions caused by birefringent walk-off cannot be eliminated.
  46. Similar but not identical results are revealed in Ref. [42].
  47. The measured ratio of the |HH⟩ and |VV⟩ components in each entangled-photon pair is 1.31, 1.29, 1.31, 0.77, and 0.76, respectively, when bandpass filters were absent. The imbalance even got server when using bandpass filters since signal photons in these two components possess different FWHM values.
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    [Crossref]
  49. O. Gühne, C.-Y. Lu, W.-B. Gao, and J.-W. Pan, “Toolbox for entanglement detection and fidelity estimation,” Phys. Rev. A 76, 030305 (2007).
    [Crossref]
  50. G. Tóth and O. Gühne, “Detecting genuine multipartite entanglement with two local measurements,” Phys. Rev. Lett. 94, 060501 (2005).
    [Crossref]
  51. Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phys. Rev. A 84, 062118 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref]
  54. S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843–845 (2001).
    [Crossref]
  55. The maximal collinear deffII is calculated to be equal to 2.02  pm/V in Ref. [42].
  56. Parts of similar results can been found in Ref. [42].
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    [Crossref]

2016 (2)

H. Lu, Z. Zhang, L.-K. Chen, Z.-D. Li, C. Liu, L. Li, N.-L. Liu, X. Ma, Y.-A. Chen, and J.-W. Pan, “Secret sharing of a quantum state,” Phys. Rev. Lett. 117, 030501 (2016).
[Crossref]

X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li, H. Lu, Y. Hu, X. Jiang, C.-Z. Peng, L. Li, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, and J.-W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117, 210502 (2016).
[Crossref]

2015 (2)

J. Carolan, C. Harrold, C. Sparrow, E. Martn-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711–716 (2015).
[Crossref]

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
[Crossref]

2014 (2)

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvao, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
[Crossref]

2013 (5)

X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, M. Gu, M.-J. Zhu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110, 230501 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

2012 (5)

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[Crossref]

X.-C. Yao, T.-X. Wang, H.-Z. Chen, W.-B. Gao, A. G. Fowler, R. Raussendorf, Z.-B. Chen, N.-L. Liu, C.-Y. Lu, Y.-J. Deng, Y.-A. Chen, and J.-W. Pan, “Experimental demonstration of topological error correction,” Nature 482, 489–494 (2012).
[Crossref]

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

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
[Crossref]

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

2011 (3)

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger-Horne-Zeilinger state,” Nat. Commun. 2, 546 (2011).
[Crossref]

A. Halevy, E. Megidish, L. Dovrat, H. Eisenberg, P. Becker, and L. Bohatý, “The biaxial nonlinear crystal BiB3O6 as a polarization entangled photon source using non-collinear type-II parametric down-conversion,” Opt. Express 19, 20420–20434 (2011).
[Crossref]

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phys. Rev. A 84, 062118 (2011).
[Crossref]

2010 (1)

Z.-S. Yuan, X.-H. Bao, C.-Y. Lu, J. Zhang, C.-Z. Peng, and J.-W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

2009 (2)

W. Laskowski, M. Wieśniak, M. Żukowski, M. Bourennane, and H. Weinfurter, “Interference contrast in multisource few-photon optics,” J. Phys. B 42, 114004 (2009).
[Crossref]

R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express 17, 18920–18933 (2009).
[Crossref]

2008 (3)

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse Gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[Crossref]

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[Crossref]

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[Crossref]

2007 (6)

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[Crossref]

C.-Y. Lu, D. E. Browne, T. Yang, and J.-W. Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits,” Phys. Rev. Lett. 99, 250504 (2007).
[Crossref]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (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]

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[Crossref]

O. Gühne, C.-Y. Lu, W.-B. Gao, and J.-W. Pan, “Toolbox for entanglement detection and fidelity estimation,” Phys. Rev. A 76, 030305 (2007).
[Crossref]

2006 (1)

I. Pinelis, “On normal domination of (super) martingales,” Electron. J. Probab. 11, 1049–1070 (2006).
[Crossref]

2005 (2)

G. Tóth and O. Gühne, “Detecting genuine multipartite entanglement with two local measurements,” Phys. Rev. Lett. 94, 060501 (2005).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

2004 (2)

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

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[Crossref]

2003 (1)

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301 (2003).
[Crossref]

2002 (1)

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

2001 (4)

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

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref]

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

1999 (1)

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1996 (1)

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198–201 (1996).
[Crossref]

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]

1987 (1)

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

Aaronson, S.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

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H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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H. Lu, Z. Zhang, L.-K. Chen, Z.-D. Li, C. Liu, L. Li, N.-L. Liu, X. Ma, Y.-A. Chen, and J.-W. Pan, “Secret sharing of a quantum state,” Phys. Rev. Lett. 117, 030501 (2016).
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H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, M. Gu, M.-J. Zhu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110, 230501 (2013).
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V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
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X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li, H. Lu, Y. Hu, X. Jiang, C.-Z. Peng, L. Li, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, and J.-W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117, 210502 (2016).
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C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvao, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
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J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
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W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001).
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M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
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P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
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X.-C. Yao, T.-X. Wang, H.-Z. Chen, W.-B. Gao, A. G. Fowler, R. Raussendorf, Z.-B. Chen, N.-L. Liu, C.-Y. Lu, Y.-J. Deng, Y.-A. Chen, and J.-W. Pan, “Experimental demonstration of topological error correction,” Nature 482, 489–494 (2012).
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X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
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X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li, H. Lu, Y. Hu, X. Jiang, C.-Z. Peng, L. Li, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, and J.-W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117, 210502 (2016).
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X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
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X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, M. Gu, M.-J. Zhu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110, 230501 (2013).
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J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
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J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
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D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
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D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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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).
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W. Laskowski, M. Wieśniak, M. Żukowski, M. Bourennane, and H. Weinfurter, “Interference contrast in multisource few-photon optics,” J. Phys. B 42, 114004 (2009).
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J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
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R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
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X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
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X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li, H. Lu, Y. Hu, X. Jiang, C.-Z. Peng, L. Li, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, and J.-W. Pan, “Experimental ten-photon entanglement,” Phys. Rev. Lett. 117, 210502 (2016).
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X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
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Wu, Y.-P.

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
[Crossref]

Xu, P.

H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
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X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
[Crossref]

Yang, T.

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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C.-Y. Lu, D. E. Browne, T. Yang, and J.-W. Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits,” Phys. Rev. Lett. 99, 250504 (2007).
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Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
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Yao, X.-C.

H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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X.-C. Yao, T.-X. Wang, H.-Z. Chen, W.-B. Gao, A. G. Fowler, R. Raussendorf, Z.-B. Chen, N.-L. Liu, C.-Y. Lu, Y.-J. Deng, Y.-A. Chen, and J.-W. Pan, “Experimental demonstration of topological error correction,” Nature 482, 489–494 (2012).
[Crossref]

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
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Yin, H.

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
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Yin, J.

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
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J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
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Yuan, Z.-S.

Z.-S. Yuan, X.-H. Bao, C.-Y. Lu, J. Zhang, C.-Z. Peng, and J.-W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
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C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref]

J.-W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
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D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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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).
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Zhang, A.-N.

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[Crossref]

Zhang, J.

Z.-S. Yuan, X.-H. Bao, C.-Y. Lu, J. Zhang, C.-Z. Peng, and J.-W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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Zhang, Q.

K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
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Zhang, Y.

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phys. Rev. A 84, 062118 (2011).
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Zhang, Z.

H. Lu, Z. Zhang, L.-K. Chen, Z.-D. Li, C. Liu, L. Li, N.-L. Liu, X. Ma, Y.-A. Chen, and J.-W. Pan, “Secret sharing of a quantum state,” Phys. Rev. Lett. 117, 030501 (2016).
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Zhao, B.

H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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Zhao, Z.

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
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Zhou, F.

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
[Crossref]

Zhou, X.-Q.

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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Zhu, M.-J.

X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, M. Gu, M.-J. Zhu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Experimental quantum computing to solve systems of linear equations,” Phys. Rev. Lett. 110, 230501 (2013).
[Crossref]

Zukowski, M.

W. Laskowski, M. Wieśniak, M. Żukowski, M. Bourennane, and H. Weinfurter, “Interference contrast in multisource few-photon optics,” J. Phys. B 42, 114004 (2009).
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J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
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W. Laskowski, M. Wieśniak, M. Żukowski, M. Bourennane, and H. Weinfurter, “Interference contrast in multisource few-photon optics,” J. Phys. B 42, 114004 (2009).
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Nat. Commun. (1)

Y.-F. Huang, B.-H. Liu, L. Peng, Y.-H. Li, L. Li, C.-F. Li, and G.-C. Guo, “Experimental generation of an eight-photon Greenberger-Horne-Zeilinger state,” Nat. Commun. 2, 546 (2011).
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Nat. Photonics (5)

X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-S. Pan, X.-H. Bao, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, and J.-W. Pan, “Observation of eight-photon entanglement,” Nat. Photonics 6, 225–228 (2012).
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M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
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A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
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N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvao, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

H. Lu, L.-K. Chen, C. Liu, P. Xu, X.-C. Yao, L. Li, N.-L. Liu, B. Zhao, Y.-A. Chen, and J.-W. Pan, “Experimental realization of a concatenated Greenberger-Horne-Zeilinger state for macroscopic quantum superpositions,” Nat. Photonics 8, 364–368 (2014).
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Nat. Phys. (1)

C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
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Nature (10)

Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
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X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
[Crossref]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012).
[Crossref]

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
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R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[Crossref]

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
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P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
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Other (10)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

The twofold coincidence counting rate of entangled-photon pairs, also known as the brightness of entangled-photon pairs, can be described as RTξ2, while entanglement decays with ∼O(1/RT).

S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” in Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (ACM, 2011), pp. 333–342.

The maximal collinear deffII is calculated to be equal to 2.02  pm/V in Ref. [42].

Parts of similar results can been found in Ref. [42].

Periodically poled KTiOPO4 (ppKTP) can also meet the two requirements. However, the strong frequency correlation in our interested wavelength range prevents ppKTP from being an appropriate candidate for the demonstration of multi-photon entanglement.

The spatial walk-offs result in the decay of beam quality, reducing the SPDC photons’ collection efficiency.

The two birefringent compensators make the SPDC photons overlap in spatio-temporal mode. However, the distortions caused by birefringent walk-off cannot be eliminated.

Similar but not identical results are revealed in Ref. [42].

The measured ratio of the |HH⟩ and |VV⟩ components in each entangled-photon pair is 1.31, 1.29, 1.31, 0.77, and 0.76, respectively, when bandpass filters were absent. The imbalance even got server when using bandpass filters since signal photons in these two components possess different FWHM values.

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Figures (4)

Fig. 1.
Fig. 1.

Numerical simulations for the SPDC photon rings through a 3 nm bandpass filter. (a) Different polarizations of the birefringent rays in a BiBO crystal. The blue (red) ring represents the spatial distribution of the signal (idler) photons. If the vector that connects the two intersections of the SPDC rings is parallel to H, the F (S) has a 15° deflection from H (V) [46], which can be calculated using the electric field vector E for the 390  nm780  nm type-II SPDC process. (b) Respective SPDC photon rings of BBO and BiBO crystals. The wave vector k is solely used to describe the spatial distributions within the system. In this simulation, the FWHM of the pump laser is assumed to be approximately 2.1 nm.

Fig. 2.
Fig. 2.

Experimental setup for preparing ten-photon GHZ state. An ultrafast pump laser with a central wavelength of 390 nm and a FWHM of 2.1 nm is successively sent through the BiBO crystals to generate polarization-entangled photon pairs, i.e., EPR1EPR5. The distance between the first and fifth BiBO crystals is 2.65 m. In each BiBO-based Bell state synthesizer architecture, lenses with the focal length of 400 mm are placed to maximize the ξ. The polarization of each output photon is analyzed using a combination of a quarter-wave plate (QWP), a HWP, and a PBS, together with a single-mode, fiber-coupled SPCM in each output of the PBS. Bandpass filters with ΔλFWHMfilter·s=3.6  nm on paths 2, 3, 5, 7, and 9 are used to erase the time information between the five entangled photon pairs [44]. The other bandpass filters with ΔλFWHMfilter·i=7.8  nm are chosen to achieve a maximum ξ. We engineer these five entangled photon pairs into a ten-photon GHZ state by combining five signal photons on a linear optical network consisting of four PBSs.

Fig. 3.
Fig. 3.

Experimental results for the ten-photon GHZ state. (a) Population of the prepared tenfold coincidence events in the H/V basis. The total measured time is 300 h. (b) Expectation values in the basis of Mk10, k=0,1,,9. The M0(σx) and M5(σy) values are measured, respectively, for 110 h, while the remaining eight observables are measured for 80 h. Error bars indicate one standard deviation deduced from propagated Poissonian counting statistics of the raw detection events.

Fig. 4.
Fig. 4.

Theoretical simulation curves of the collinear type-II phase-matching angles, deffII, and the spatial walk-off for a BiBO crystal. The collinear type-II phase-matching angles (θ,ϕ) in the main refractive index coordinates (solid red), deffII (dotted blue), δθ of 780 nm slow (dashed black) and fast (dashed gray) photons are simulated, respectively. The yellow dot represents the non-collinear type-II phase-matching angle (1.944, 0.962 rad) used in the experiment.

Tables (4)

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Table 1. Experimental Relationship Between the Increase of ξ and Decrease of the Spatial Walk-Off Value

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Table 2. Experimental Relative RT Under Different Bandpass Filtersa

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Table 3. Theoretical Values of np, ns, ni, and Δ in BBO and BiBO Crystals

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Table 4. Tenfold Coincidence Counting Events in the H/V and Mk10 Bases

Equations (9)

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|GHZ10=12(|H10+|V10).
F^=|GHZnGHZn|=12(|Hn+|Vn)(H|n+V|n)=k=0n1αkMkn+12((|HH|)n+(|VV|)n),
F¯=k=0n1αkNk+NkNk+12Nz0+Nz1Nz.
RT,(deffBiBOdeffBBO)2·LBiBOLBBO·[npnsni(nins)]BBO[npnsni(nins)]BiBO·ΩBiBOΩBBO.
F¯est=1Nti=1NtFi.
FbsK=i=1K(FiF0),
p=Probbs(F¯bsF¯exp)D(Nt(F¯expF0)SNt),
SNt=i=1Ntsi2,=(Nt4Nz)2×Nz+k=09(αkNtNk)2×Nk,=Nt116Nz+k=09αk2Nk.
p=Probbs(F¯bsF¯exp)D((F¯expF0)116Nz+k=09αk2Nk).

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