Abstract

We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Direct production of three-color polarization entanglement for continuous variable

Zhihui Yan and Xiaojun Jia
J. Opt. Soc. Am. B 32(10) 2139-2145 (2015)

Entanglement in a four-wave mixing process

Zhan Zheng, Hailong Wang, Bing Cheng, and Jietai Jing
Opt. Lett. 42(14) 2754-2757 (2017)

References

  • View by:
  • |
  • |
  • |

  1. A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
    [Crossref]
  2. D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
    [Crossref]
  3. C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
    [Crossref]
  4. J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
    [Crossref] [PubMed]
  5. T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
    [Crossref] [PubMed]
  6. H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
    [Crossref] [PubMed]
  7. Peter v. Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
    [Crossref] [PubMed]
  8. S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
    [Crossref]
  9. J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
    [Crossref]
  10. S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
    [Crossref] [PubMed]
  11. M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
    [Crossref] [PubMed]
  12. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [Crossref] [PubMed]
  13. R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
    [Crossref] [PubMed]
  14. V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
    [Crossref]
  15. Peter v. Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [Crossref]
  16. R. F. Werner and M. M. Wolf, “Bound Entangled Gaussian States,” Phys. Rev. Lett. 86, 3658–3661 (2001).
    [Crossref] [PubMed]
  17. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
    [Crossref] [PubMed]
  18. A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
    [Crossref] [PubMed]
  19. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
    [Crossref] [PubMed]
  20. J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
    [Crossref]
  21. F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).
  22. J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
    [Crossref]
  23. Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
    [Crossref] [PubMed]
  24. K. N. Cassemiro and A. S. Villar, “Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators,” Phys. Rev. A 77, 022311 (2008).
    [Crossref]
  25. A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
    [Crossref]
  26. X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
    [Crossref]
  27. H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
    [Crossref] [PubMed]
  28. L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
    [Crossref]
  29. F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
    [Crossref]
  30. F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
    [Crossref]
  31. A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
    [Crossref] [PubMed]

2015 (1)

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

2014 (5)

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

2013 (2)

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

2012 (3)

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
[Crossref]

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

2011 (2)

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

2010 (2)

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

2009 (3)

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

2008 (2)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

K. N. Cassemiro and A. S. Villar, “Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators,” Phys. Rev. A 77, 022311 (2008).
[Crossref]

2004 (1)

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

2003 (4)

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Peter v. Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

2001 (1)

R. F. Werner and M. M. Wolf, “Bound Entangled Gaussian States,” Phys. Rev. Lett. 86, 3658–3661 (2001).
[Crossref] [PubMed]

2000 (3)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[Crossref] [PubMed]

Peter v. Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

1993 (1)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Aoki, T.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Armstrong, S. C.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Barbosa, F. A. S.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

Boyer, V.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Braunstein, S. L.

Peter v. Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

Cai, Y.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

Cao, L.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

Cassemiro, K. N.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

K. N. Cassemiro and A. S. Villar, “Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators,” Phys. Rev. A 77, 022311 (2008).
[Crossref]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Chen, M.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Clark, J. B.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Coelho, A. S.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

de Araújo, R. M.

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

de Faria, A. J.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Duan, Z

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Fabre, C.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

Fedrizzi, A.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Furusawa, A.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Peter v. Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

Gerke, S.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Glasser, R. T.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Glorieux, Q.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
[Crossref]

Hamel, D. R.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Hiraoka, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Horne, M. A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
[Crossref]

Hübel, H.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Hudelist, F.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

Jennewein, T.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Jia, X.

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Jiang, S. F.

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

Jing, J.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Jones, K. M.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

Kaji, T.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

Lett, P. D.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Li, T.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Liu, C.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Loock, Peter v.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Peter v. Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

Peter v. Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

Mancini, S.

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Marino, A. M.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Martinelli, M.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

Menicucci, N. C.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Nussenzveig, P.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

Ou, Z. Y.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Patrón, R. G.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Peng, K.

A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
[Crossref]

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Pfister, O.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Pooser, R. C.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Qin, Z.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Ramelow, S.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Resch, K. J.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Roslund, J.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

Shalm, L. K.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Simon, C.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

Simon, R.

R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[Crossref] [PubMed]

Sornphiphatphong, C.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Sperling, J.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

Su, X.

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Suzuki, S.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Takei, N.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Tan, A.

A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
[Crossref]

Tombesi, P.

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Treps, N.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

Ukai, R.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Villar, A. S.

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

K. N. Cassemiro and A. S. Villar, “Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators,” Phys. Rev. A 77, 022311 (2008).
[Crossref]

Vitali, D.

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Vogel, W.

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

Vogl, U.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

Wakui, K.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Wang, H.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Werner, R. F.

R. F. Werner and M. M. Wolf, “Bound Entangled Gaussian States,” Phys. Rev. Lett. 86, 3658–3661 (2001).
[Crossref] [PubMed]

Wolf, M. M.

R. F. Werner and M. M. Wolf, “Bound Entangled Gaussian States,” Phys. Rev. Lett. 86, 3658–3661 (2001).
[Crossref] [PubMed]

Xie, C.

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
[Crossref]

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Yan, Y.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Yan, Z.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Yokoyama, S.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Yonezawa, H.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Yoshikawa, J. I.

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

Zeilinger, A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
[Crossref]

Zhang, J.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Zhang, W.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Zhao, F.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Zhou, Z.

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99, 011110 (2011).
[Crossref]

Nature (3)

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref] [PubMed]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[Crossref] [PubMed]

Nature Commun. (1)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nature Commun. 5, 3049 (2014).

Nature Photon. (4)

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nature Photon. 8, 515–519 (2014).
[Crossref]

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Robustness of bipartite Gaussian entangled beams propagating in lossy channels,” Nature Photon. 4, 858–861 (2010).
[Crossref]

S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J. I. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, “Ultra-large-scale continuous-variable cluster states multiplexed in the time domain,” Nature Photon. 7, 982–986 (2013).
[Crossref]

J. Roslund, R. M. de Araújo, S. F. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nature Photon. 8, 109–112 (2014).
[Crossref]

Nature Phys. (1)

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy-time entanglement,” Nature Phys. 9, 19–22 (2013).
[Crossref]

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Phys. Rev. A (5)

V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, “Characterizing the entanglement of bipartite quantum systems,” Phys. Rev. A 67, 022320 (2003).
[Crossref]

Peter v. Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, and M. Martinelli, “Disentanglement in bipartite continuous-variable systems,” Phys. Rev. A 84, 052330 (2011).
[Crossref]

K. N. Cassemiro and A. S. Villar, “Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators,” Phys. Rev. A 77, 022311 (2008).
[Crossref]

A. Tan, C. Xie, and K. Peng, “Bright three-color entangled state produced by cascaded optical parametric oscillators,” Phys. Rev. A 85, 013819 (2012).
[Crossref]

Phys. Rev. Lett. (11)

X. Jia, Z. Yan, Z Duan, X. Su, H. Wang, C. Xie, and K. Peng, “Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths,” Phys. Rev. Lett. 109, 253604 (2012).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113, 023602 (2014).
[Crossref] [PubMed]

R. F. Werner and M. M. Wolf, “Bound Entangled Gaussian States,” Phys. Rev. Lett. 86, 3658–3661 (2001).
[Crossref] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-Noise Amplification of a Continuous-Variable Quantum State,” Phys. Rev. Lett. 103, 010501 (2009).
[Crossref] [PubMed]

Peter v. Loock and S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental Demonstration of Tripartite Entanglement and Controlled Dense Coding for Continuous Variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and Peter v. Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre, “Full Multipartite Entanglement of Frequency-Comb Gaussian States,” Phys. Rev. Lett. 114, 050501 (2015).
[Crossref] [PubMed]

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[Crossref] [PubMed]

Phys. Today (1)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Multiparticle Interferometry and the Superposition Principle,” Phys. Today 46, 22–29 (1993).
[Crossref]

Rev. Mod. Phys. (1)

C. Weedbrook, S. Pirandola, R. G. Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[Crossref]

Science (2)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-Color Entanglement,” Science 326, 823–826 (2009).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Proposed schemes for generating tripartite entanglement based on the cascaded FWM processes. (a) Cascaded FWM processes, â0 is coherent input signal, âν1 and âν2 are vacuum inputs, G1 and G2 are the power gains of cell1 and cell2, respectively. â1, â2 and â3 are three output beams. (b) Energy level diagram of 85Rb D1 line for the single FWM process. 0.8 GHz is one-photon detuning, 4 MHz is two-photon detuning. (c) Another cascaded FWM processes.

Fig. 2
Fig. 2

(a) Region plot of Eq. (7). Region A is a region where D23 <4, region B is a region where D12 <4, region C is a region where D12, D13 and D23 in Eq. (7) are all falling above 4; (b) The contour plot of D12; and (c) The contour plot of D23.

Fig. 3
Fig. 3

The contour plot of (a) B1; and (b) B2; and (c) B3.

Fig. 4
Fig. 4

(a) The contour plot of V12; (b) The contour plot of V23; and (c) The light blue region is the region of V23 <4, the light orange region is the region of V12<4.

Fig. 5
Fig. 5

The contour plot for V213 in Eq. (16).

Fig. 6
Fig. 6

(a) The contour plot of V 213 opt in Eq. (17); (b) The dependence of V 213 opt (trace A); 2 ( | F 1 2 | + | 1 F 3 2 | ) (trace B); 2 ( | F 3 2 | + | 1 F 1 2 | ) (trace C); and 2 ( 1 + | F 1 2 + F 3 2 | ) (trace D) on gain G; and (c) The dependence of R on gain G. 1 for trace A, R = V 213 opt / 2 ( | F 1 2 | + | 1 F 3 2 | ) for trace B.

Fig. 7
Fig. 7

The contour plot of (a) T1; (b) T2; and (c) T3.

Equations (21)

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

X ^ k = a ^ k + a ^ k , Y ^ k = i ( a ^ k a ^ k ) ,
a ^ 1 = G 1 a ^ ν 1 + g 1 a ^ 0 , a ^ 2 = G 1 G 2 a ^ 0 + G 2 g 1 a ^ ν 1 + g 2 a ^ ν 2 , a ^ 3 = G 2 a ^ ν 2 + G 1 g 2 a ^ 0 + g 1 g 2 a ^ ν 1 ,
( X ^ 1 X ^ 2 X ^ 3 ) = ( G 1 g 1 0 G 2 g 1 G 1 G 2 g 2 g 1 g 2 G 1 g 2 G 2 ) ( X ^ ν 1 X ^ 0 X ^ ν 2 ) ,
( Y ^ 1 Y ^ 2 Y ^ 3 ) = ( G 1 g 1 0 G 2 g 1 G 1 G 2 g 2 g 1 g 2 G 1 g 2 G 2 ) ( Y ^ ν 1 Y ^ 0 Y ^ ν 2 ) .
X ^ 1 2 = Y ^ 1 2 = 2 G 1 , X ^ 2 2 = Y ^ 2 2 = 2 G 1 G 2 1 , X ^ 3 2 = Y ^ 3 2 = 2 G 1 G 2 2 G 1 + 1 ,
X ^ 1 X ^ 2 = Y ^ 1 Y ^ 2 = 2 G 1 G 2 ( G 1 1 ) , X ^ 1 X ^ 3 = Y ^ 1 Y ^ 3 = 2 G 1 ( G 1 1 ) ( G 2 1 ) , X ^ 2 X ^ 3 = Y ^ 2 Y ^ 3 = 2 G 1 G 2 ( G 2 1 ) ,
D 12 = V ( X ^ 1 X ^ 2 ) + V ( Y ^ 1 + Y ^ 2 ) 4 , D 13 = V ( X ^ 1 X ^ 3 ) + V ( Y ^ 1 + Y ^ 3 ) 4 , D 23 = V ( X ^ 2 X ^ 3 ) + V ( Y ^ 2 + Y ^ 3 ) 4 .
D 12 = 4 [ G 1 ( G 2 + 1 ) 2 G 1 G 2 ( G 1 1 ) 1 ] , D 13 = 4 G 1 G 2 , D 23 = 4 [ 2 G 1 G 2 2 G 1 G 2 ( G 2 1 ) G 1 ] .
CM 12 = [ X ^ 1 2 0 X ^ 1 X ^ 2 0 0 Y ^ 1 2 0 Y ^ 1 Y ^ 2 X ^ 1 X ^ 2 0 X ^ 2 2 0 0 Y ^ 1 Y ^ 2 0 Y ^ 2 2 ] .
B 1 = 1 + G 1 + G 1 G 2 G 1 2 4 G 1 G 2 + 2 G 1 2 G 2 + G 1 2 G 2 2 ,
B 2 = G 1 + 2 G 1 G 2 ( 1 2 G 1 ) + ( G 1 + 2 G 1 G 2 ) 2 ,
B 3 = 1 + 2 G 1 G 1 G 2 + ( 1 2 G 1 + G 1 G 2 ) 2 ( 1 2 G 1 G 2 ) ,
V 12 = V ( X ^ 1 X ^ 2 ) + V ( Y ^ 1 + Y ^ 2 + O 3 Y ^ 3 ) 4 , V 23 = V ( X ^ 2 X ^ 3 ) + V ( O 1 Y ^ 1 + Y ^ 2 + Y ^ 3 ) 4 ,
O 1 opt = ( Y ^ 1 Y ^ 2 + Y ^ 1 Y ^ 3 ) Y ^ 1 2 = 2 G 1 G 2 ( G 1 1 ) 2 G 1 ( G 1 1 ) ( G 2 1 ) 2 G 1 1 , O 3 opt = ( Y ^ 1 Y ^ 3 + Y ^ 2 Y ^ 3 ) Y ^ 3 2 = 2 G 1 G 2 ( G 2 1 ) 2 G 1 ( G 1 1 ) ( G 2 1 ) 2 G 1 G 2 2 G 1 + 1 ,
V 213 = V [ X ^ 2 1 2 ( X ^ 1 + X ^ 3 ) ] + V [ Y ^ 2 + 1 2 ( Y ^ 1 + Y ^ 3 ) ] , V 312 = V [ X ^ 3 1 2 ( X ^ 1 + X ^ 2 ) ] + V [ Y ^ 3 + 1 2 ( Y ^ 1 + Y ^ 2 ) ] , V 123 = V [ X ^ 1 1 2 ( X ^ 2 + X ^ 3 ) ] + V [ Y ^ 1 + 1 2 ( Y ^ 2 + Y ^ 3 ) ] .
V 213 = 2 [ G 2 1 G 2 2 ] 2 + 2 [ ( G 1 1 ) G 2 G 1 2 ( G 1 1 ) ( G 2 1 ) 2 ] 2 + 2 [ G 1 G 2 G 1 1 2 G 1 ( G 2 1 ) 2 ] 2 .
V 213 opt = V [ X ^ 2 F 1 X ^ 1 F 3 X ^ 3 ] + V [ Y ^ 2 + F 1 Y ^ 1 + F 3 Y ^ 3 ] ,
F 1 opt = Y ^ 1 Y ^ 2 Y ^ 3 2 Y ^ 1 Y ^ 3 Y ^ 2 Y ^ 3 Y ^ 1 Y ^ 3 2 Y ^ 1 2 Y ^ 3 2 , F 3 opt = Y ^ 2 Y ^ 3 Y ^ 1 2 Y ^ 1 Y ^ 3 Y ^ 1 Y ^ 2 Y ^ 1 Y ^ 3 2 Y ^ 1 2 Y ^ 3 2 .
V 213 opt = 2 2 G 2 1 ,
F 1 opt = 2 G G 1 2 G 2 1 , F 3 opt = 2 G G ( G 1 ) 2 G 2 1 ,
CM 123 = [ X ^ 1 2 0 X ^ 1 X ^ 2 0 X ^ 1 X ^ 3 0 0 Y ^ 1 2 0 Y ^ 1 Y ^ 2 0 Y ^ 1 Y ^ 3 X ^ 1 X ^ 2 0 X ^ 2 2 0 X ^ 2 X ^ 3 0 0 Y ^ 1 Y ^ 2 0 Y ^ 2 2 0 Y ^ 2 Y ^ 3 X ^ 1 X ^ 3 0 X ^ 2 X ^ 3 0 X ^ 3 2 0 0 Y ^ 1 Y ^ 3 0 Y ^ 2 Y ^ 3 0 Y ^ 3 2 ] .

Metrics