OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 3 — Mar. 1, 2010
  • pp: 447–451

Tripartite entanglement in parametric down-conversion with spatially structured pump

D. Daems, F. Bernard, N. J. Cerf, and M. I. Kolobov  »View Author Affiliations

JOSA B, Vol. 27, Issue 3, pp. 447-451 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (116 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field and have neglected its spatial structure. We present a simple model which allows us to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2 N + 1 partite entanglement using 2 N symmetrically tilted plane pump waves. Another interesting feature is the possibility of entanglement localization in just two spatial modes.

© 2010 Optical Society of America

OCIS Codes
(270.6570) Quantum optics : Squeezed states
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: November 13, 2009
Revised Manuscript: January 21, 2010
Manuscript Accepted: January 21, 2010
Published: February 16, 2010

D. Daems, F. Bernard, N. J. Cerf, and M. I. Kolobov, "Tripartite entanglement in parametric down-conversion with spatially structured pump," J. Opt. Soc. Am. B 27, 447-451 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61, 052306 (2006). [CrossRef]
  2. G. Adesso, A. Serafini, and F. Illuminati, “Quantification and scaling of multipartite entanglement in continuous variable systems,” Phys. Rev. Lett. 93, 220504 (2004). [CrossRef] [PubMed]
  3. A. Serafini, G. Adesso, and F. Illuminati, “Unitarily localizable entanglement of Gaussian states,” Phys. Rev. A 71, 032349 (2005). [CrossRef]
  4. G. Adesso, A. Serafini, and F. Illuminati, “Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence,” Phys. Rev. A 73, 032345 (2006). [CrossRef]
  5. G. Adesso and F. Illuminati, “Bipartite and multipartite entanglement of Gaussian states,” in Quantum Information with Continuous Variables of Atoms and Light, N.J.Cerf, G.Leuchs, and E.S.Polzik, eds. (Imperial College Press, 2007), pp. 1-21. [CrossRef]
  6. T. J. Osborne and F. Verstraete, “General monogamy inequality for bipartite qubit entanglement,” Phys. Rev. Lett. 96, 220503 (2006). [CrossRef] [PubMed]
  7. T. Hiroshima, G. Adesso, and F. Illuminati, “Monogamy inequality for distributed Gaussian entanglement,” Phys. Rev. Lett. 98, 050503 (2007). [CrossRef] [PubMed]
  8. Y. Lian, C. Xie, and K. Peng, “Continuous variable multipartite entanglement and optical implementations of quantum communication networks,” New J. Phys. 9, 314 (2007). [CrossRef]
  9. P. van Loock and S. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482 (2000). [CrossRef] [PubMed]
  10. O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004). [CrossRef]
  11. J. Guo, H. Zou, Z. Zhai, J. Zhang, and J. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005). [CrossRef]
  12. Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasiperiodic superlattice,” Phys. Rev. A 74, 042332 (2006). [CrossRef]
  13. A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241-1249 (2004). [CrossRef]
  14. M. K. Olsen and A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74, 063809 (2006). [CrossRef]
  15. A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253-256 (2004). [CrossRef]
  16. M. N. O'Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: Experimental realization of optically entangled d=3 and d=6 qudits,” Phys. Rev. Lett. 94, 220501 (2005). [CrossRef] [PubMed]
  17. M. Stütz, S. Groblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. 90, 261114 (2007). [CrossRef]
  18. P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005). [CrossRef]
  19. J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. 't Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008). [CrossRef] [PubMed]
  20. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003). [CrossRef]
  21. M. I. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539-1589 (1999). [CrossRef]
  22. A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413 (1996). [CrossRef] [PubMed]
  23. M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1-8 (1996). [CrossRef]
  24. R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726 (2000). [CrossRef] [PubMed]
  25. R. F. Werner and M. M. Wolf, “Bound entangled Gaussian states,” Phys. Rev. Lett. 86, 3658 (2001). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited