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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26351–26362

Experimental characterization of two spatial qutrits using entanglement witnesses

A. J. Gutiérrez-Esparza, W. M. Pimenta, B. Marques, A. A. Matoso, J. L. Lucio M., and S. Pádua  »View Author Affiliations

Optics Express, Vol. 20, Issue 24, pp. 26351-26362 (2012)

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We present an experimental technique for a complete characterization of entanglement in a two-qutrit state generated using transverse spatial correlations of two parametric down-converted photons. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables of single path and superposition projection operators. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter which allow to modulate the amplitude of individually chosen path states. The quantification of entanglement is computed by the negativity obtained from the expectation values of the entanglement witnesses implemented.

© 2012 OSA

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5565) Quantum optics : Quantum communications
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: August 21, 2012
Revised Manuscript: October 19, 2012
Manuscript Accepted: October 20, 2012
Published: November 7, 2012

A. J. Gutiérrez-Esparza, W. M. Pimenta, B. Marques, A. A. Matoso, J. L. Lucio M., and S. Pádua, "Experimental characterization of two spatial qutrits using entanglement witnesses," Opt. Express 20, 26351-26362 (2012)

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  1. A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett.77, 1413–1415 (1996). [CrossRef] [PubMed]
  2. M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A223, 1–8 (1996). [CrossRef]
  3. B. Terhal, “Bell inequalities and the separability criterion,” Phys. Lett. A271, 319–326 (2000). [CrossRef]
  4. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A62, 052310 (2000). [CrossRef]
  5. O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, “Experimental detection of entanglement via witness operators and local measurements,” J. Mod. Opt.50, 1079–1102 (2003). [CrossRef]
  6. M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. D’Ariano, and C. Macchiavello, “Detection of entanglement with polarized photons: experimental realization of an entanglement witness,” Phys. Rev. Lett.91, 227901 (2003). [CrossRef] [PubMed]
  7. M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett.92, 87902 (2004). [CrossRef]
  8. N. Kiesel, C. Schmid, U. Weber, G. Tóth, O. Gühne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett.95, 210502 (2005). [CrossRef] [PubMed]
  9. O. Gühne and G. Tóth, “Entanglement detection,” Physics Reports474, 1–75 (2009). [CrossRef]
  10. After submission of this work we became aware of an entanglement witness measurement in high dimensional orbital angular momentum states: M. Agnew, J. Leach, and R.W. Boyd, “Observation of entanglement witnesses for orbital angular momentum states,” Eur. Phys. J. D66, 1–4 (2012). [CrossRef]
  11. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75 (2006). [CrossRef]
  12. R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A34, 3962–3968 (1986). [CrossRef] [PubMed]
  13. Z. Y. Ou and L. Mandel, “Violation of bells inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett.61, 50–53 (1988). [CrossRef] [PubMed]
  14. Y. H. Shih and C. O. Alley, “New type of einstein-podolsky-rosen-bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988). [CrossRef] [PubMed]
  15. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75, 4337–4341 (1995). [CrossRef] [PubMed]
  16. I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science328, 879–881 (2010). [CrossRef] [PubMed]
  17. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London)412, 313–316 (2001). [CrossRef]
  18. J. G. Rarity and P. R. Tapster, “Experimental violation of bells inequality based on phase and momentum,” Phys. Rev. Lett.64, 2495–2498 (1990). [CrossRef] [PubMed]
  19. A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett.102, 153902 (2009). [CrossRef] [PubMed]
  20. L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett.94, 100501 (2005). [CrossRef] [PubMed]
  21. M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric down-conversion,” Phys. Rev. Lett.99, 063901 (2007). [CrossRef] [PubMed]
  22. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett.82, 2594–2597 (1999). [CrossRef]
  23. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989). [CrossRef] [PubMed]
  24. A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Generation of time-bin-entangled photons without temporal postselection,” Phys. Rev. A78, 012345 (2008). [CrossRef]
  25. L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A69, 042305 (2004). [CrossRef]
  26. J. Fuchs and C. Schweigert, Symmetries, Lie algebras and representations: A graduate course for physicists (Cambridge University Press, 1997).
  27. W. M. Pimenta, B. Marques, M. A. Carvalho, M. R. Barros, J. G. Fonseca, J. Ferraz, M. Terra Cunha, and S. Pádua, “Minimal state tomography of spatial qubits using a spatial light modulator,” Opt. Express18, 24423–24433 (2010). [CrossRef] [PubMed]
  28. I. Moreno, P. Velásquez, C. Fernández-Pousa, M. Sánchez-López, and F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys.94, 3697–3702 (2003). [CrossRef]
  29. S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Physics Reports, 495, 87–139 (2010). [CrossRef]
  30. E. J. S. Fonseca, J. C. Machado da Silva, C. H. Monken, and S. Pádua, “Controlling two-particle conditional interference” Phys. Rev. A61, 023801 (2000). [CrossRef]
  31. D. Greenberger, M. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today46, 22–22 (1993). [CrossRef]
  32. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A65, 032314 (2002). [CrossRef]

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