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.

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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]
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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]
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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]
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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).
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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]

Eur. Phys. J. D

• 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]

J. Appl. Phys.

• 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]

J. Mod. Opt.

• 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]

Nature (London)

• 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]

New J. Phys.

• S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys.8, 75 (2006). [CrossRef]

Opt. Express

• 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]

Phys. Lett. A

• M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A223, 1–8 (1996). [CrossRef]
• B. Terhal, “Bell inequalities and the separability criterion,” Phys. Lett. A271, 319–326 (2000). [CrossRef]

Phys. Rev. A

• M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A62, 052310 (2000). [CrossRef]
• 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]
• L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A69, 042305 (2004). [CrossRef]
• 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]
• 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]
• G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A65, 032314 (2002). [CrossRef]

Phys. Rev. Lett.

• A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett.77, 1413–1415 (1996). [CrossRef] [PubMed]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• 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]
• J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989). [CrossRef] [PubMed]

Phys. Today

• D. Greenberger, M. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today46, 22–22 (1993). [CrossRef]

Physics Reports

• 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]
• O. Gühne and G. Tóth, “Entanglement detection,” Physics Reports474, 1–75 (2009). [CrossRef]

Science

• I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science328, 879–881 (2010). [CrossRef] [PubMed]

Other

• J. Fuchs and C. Schweigert, Symmetries, Lie algebras and representations: A graduate course for physicists (Cambridge University Press, 1997).

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