Abstract

We report on a new technique for entanglement distillation of the bipartite continuous variable state of spatially correlated photons generated in the spontaneous parametric down-conversion process (SPDC), where tunable non-Gaussian operations are implemented and the post-processed entanglement is certified in real-time using a single-photon sensitive electron multiplying CCD (EMCCD) camera. The local operations are performed using non-Gaussian filters modulated into a programmable spatial light modulator and, by using the EMCCD camera for actively recording the probability distributions of the twin-photons, one has fine control of the Schmidt number of the distilled state. We show that even simple non-Gaussian filters can be finely tuned to a ∼67% net gain of the initial entanglement generated in the SPDC process.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
[Crossref] [PubMed]

2017 (6)

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

E. Bolduc, D. Faccio, and J. Leach, “Acquisition of multiple photon pairs with an EMCCD camera,” J. Opt. 19, 054006 (2017).
[Crossref]

F. S. Roux, “Biphoton states in correlated turbulence,” Phys. Rev. A 95, 023809 (2017).
[Crossref]

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Phil. Trans. R. Soc. A 37520150442 (2017).
[Crossref] [PubMed]

H. Lai, M.-X. Luo, J. Pieprzyk, J. Zhang, L. Pan, S. Li, and M. A. Orgun, “Fast and simple high-capacity quantum cryptography with error detection,” Sci. Rep. 7, 46302 (2017).
[Crossref] [PubMed]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional Bell basis,” Optica 4, 1462 (2017).
[Crossref]

2016 (2)

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113, 13642 (2016).
[Crossref] [PubMed]

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e150116 (2016).
[Crossref]

2015 (4)

E. S. Gómez, G. Cañas, E. Acuña, W. A. T. Nogueira, and G. Lima, “Non-Gaussian-state generation certified using the Einstein-Podolsky-Rosen-steering inequality,” Phys. Rev. A 91, 013801 (2015).
[Crossref]

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons”, Nat. Comm. 6, 5913 (2015).
[Crossref]

D. Goyeneche, G. Cañas, S. Etcheverry, E. S. Gómez, G. B. Xavier, G. Lima, and A. Delgado, “Five measurement bases determine pure quantum states on any dimension,” Phys. Rev. Lett. 115, 090401 (2015).
[Crossref] [PubMed]

2014 (2)

P. -A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113, 160401 (2014).
[Crossref] [PubMed]

G. Cañas, S. Etcheverry, E. S. Gómez, C. Saavedra, G. B. Xavier, G. Lima, and A. Cabello, “Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem,” Phys. Rev. A 90, 012119 (2014).
[Crossref]

2013 (2)

F. Just, A. Cavanna, M. V. Chekhova, and G. Leuchs, “Transverse entanglement of biphotons, “New J. Phys. 15, 083015 (2013).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

2012 (3)

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
[Crossref]

E. S. Gómez, W. A. T. Nogueira, C. H. Monken, and G. Lima, “Quantifying the non-Gaussianity of the state of spatially correlated down-converted photons,” Opt. Express 20, 3753 (2012).
[Crossref] [PubMed]

M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
[Crossref]

2011 (1)

2010 (3)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Physics Reports 495, 87 (2010).
[Crossref]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Phot. 4, 227–230 (2010).
[Crossref]

A. K. Jha, G. A. Tyler, and R. W. Boyd, “Effects of atmospheric turbulence on the entanglement of spatial two-qubit states,” Phys. Rev. A 81, 053832 (2010).
[Crossref]

2009 (8)

L. J. Zhang, L. Neves, J. S. Lundeen, and I. A. Walmsley, “A characterization of the single-photon sensitivity of an electron multiplying charge-coupled device,” J. Phys. B 42, 114011 (2009).
[Crossref]

H. Di Lorenzo Pires, C. H. Monken, and M. P. van Exter, “Direct measurement of transverse-mode entanglement in two-photon states,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” EPL 87, 64003 (2009).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
[Crossref]

H. D.-L. Pires and M. P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 053820 (2009).
[Crossref]

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. Mod. Phys. 81, 299 (2009).
[Crossref]

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt. 56, 1829–1837 (2009).
[Crossref]

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Quantum entanglement beyond Gaussian criteria,” Proc. Natl. Acad. Sci. 106, 21517–21520 (2009).
[Crossref] [PubMed]

2008 (3)

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[Crossref]

A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16, 16711 (2008).
[Crossref] [PubMed]

C. I. Osorio, G. Molina-Terriza, and J. P. Torres, “Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric down-conversion,” Phys. Rev. A 77, 015810 (2008).
[Crossref]

2007 (1)

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
[Crossref]

2006 (3)

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[Crossref]

J. Zhang and S. L. Braunstein, “Continuous-variable Gaussian analog of cluster states,” Phys. Rev. A 73, 032318 (2006).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

2005 (3)

S. Braunstein and P. van Lock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
[Crossref]

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. N. O’Sullivan-Hale, I. Ali 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]

2004 (3)

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[Crossref] [PubMed]

M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, “Packet narrowing and quantum entanglement in photoionization and photodissociation,” Phys. Rev. A 69, 052117 (2004).
[Crossref]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

2003 (1)

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[Crossref] [PubMed]

2002 (2)

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[Crossref] [PubMed]

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett. 88, 120401 (2002).
[Crossref] [PubMed]

2000 (2)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722 (2000).
[Crossref] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729 (2000).
[Crossref] [PubMed]

1999 (1)

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868 (1999).
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1998 (1)

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[Crossref]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895 (1993).
[Crossref] [PubMed]

1992 (1)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881 (1992).
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1991 (1)

A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
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1989 (1)

M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913 (1989).
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1985 (1)

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409 (1985).
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1970 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden variable theories,” Phys. Rev. Lett. 24, 549 (1970).
[Crossref]

1964 (1)

J. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195 (1964).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
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Acín, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
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Acuña, E.

E. S. Gómez, G. Cañas, E. Acuña, W. A. T. Nogueira, and G. Lima, “Non-Gaussian-state generation certified using the Einstein-Podolsky-Rosen-steering inequality,” Phys. Rev. A 91, 013801 (2015).
[Crossref]

Agnew, M.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e150116 (2016).
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M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
[Crossref]

Aguirre Gómez, J. G.

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).
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Aiello, A.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
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Ali Khan, I.

M. N. O’Sullivan-Hale, I. Ali 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).
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Andrews, R.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007).
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Aspden, R. S.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons”, Nat. Comm. 6, 5913 (2015).
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Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
[Crossref] [PubMed]

Babazadeh, A.

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
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Barnett, S. M.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
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Bell, J.

J. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Bell, J. E. C.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons”, Nat. Comm. 6, 5913 (2015).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895 (1993).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881 (1992).
[Crossref] [PubMed]

Bennink, R. S.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
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Bentley, S. J.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
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Bolduc, E.

E. Bolduc, D. Faccio, and J. Leach, “Acquisition of multiple photon pairs with an EMCCD camera,” J. Opt. 19, 054006 (2017).
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Bonneau, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
[Crossref] [PubMed]

Boyd, R. W.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons”, Nat. Comm. 6, 5913 (2015).
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A. K. Jha, G. A. Tyler, and R. W. Boyd, “Effects of atmospheric turbulence on the entanglement of spatial two-qubit states,” Phys. Rev. A 81, 053832 (2010).
[Crossref]

M. N. O’Sullivan-Hale, I. Ali 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]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Boyd, R.W.

M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
[Crossref]

Brambilla, E.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
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Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895 (1993).
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Braunstein, S.

S. Braunstein and P. van Lock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
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Braunstein, S. L.

J. Zhang and S. L. Braunstein, “Continuous-variable Gaussian analog of cluster states,” Phys. Rev. A 73, 032318 (2006).
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Brida, G.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Phot. 4, 227–230 (2010).
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G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” EPL 87, 64003 (2009).
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Buchleitner, A.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
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Buchler, B.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113, 13642 (2016).
[Crossref] [PubMed]

Buller, G.S.

M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
[Crossref]

Cabello, A.

G. Cañas, S. Etcheverry, E. S. Gómez, C. Saavedra, G. B. Xavier, G. Lima, and A. Cabello, “Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem,” Phys. Rev. A 90, 012119 (2014).
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Campbell, G.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113, 13642 (2016).
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Campos, J.

Cañas, G.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

D. Goyeneche, G. Cañas, S. Etcheverry, E. S. Gómez, G. B. Xavier, G. Lima, and A. Delgado, “Five measurement bases determine pure quantum states on any dimension,” Phys. Rev. Lett. 115, 090401 (2015).
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E. S. Gómez, G. Cañas, E. Acuña, W. A. T. Nogueira, and G. Lima, “Non-Gaussian-state generation certified using the Einstein-Podolsky-Rosen-steering inequality,” Phys. Rev. A 91, 013801 (2015).
[Crossref]

G. Cañas, S. Etcheverry, E. S. Gómez, C. Saavedra, G. B. Xavier, G. Lima, and A. Cabello, “Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem,” Phys. Rev. A 90, 012119 (2014).
[Crossref]

Cardenas, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Caricato, V.

G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” EPL 87, 64003 (2009).
[Crossref]

Cariñe, J.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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Cavanna, A.

F. Just, A. Cavanna, M. V. Chekhova, and G. Leuchs, “Transverse entanglement of biphotons, “New J. Phys. 15, 083015 (2013).
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Chan, K. W.

M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, “Packet narrowing and quantum entanglement in photoionization and photodissociation,” Phys. Rev. A 69, 052117 (2004).
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Chekhova, M. V.

F. Just, A. Cavanna, M. V. Chekhova, and G. Leuchs, “Transverse entanglement of biphotons, “New J. Phys. 15, 083015 (2013).
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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 (2000).
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Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden variable theories,” Phys. Rev. Lett. 24, 549 (1970).
[Crossref]

Connolly, P. W. R.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895 (1993).
[Crossref] [PubMed]

Delgado, A.

D. Goyeneche, G. Cañas, S. Etcheverry, E. S. Gómez, G. B. Xavier, G. Lima, and A. Delgado, “Five measurement bases determine pure quantum states on any dimension,” Phys. Rev. Lett. 115, 090401 (2015).
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G. Lima, L. Neves, R. Guzmán, E. S. Gómez, W. A. T. Nogueira, A. Delgado, A. Vargas, and C. Saavedra, “Experimental quantum tomography of photonic qudits via mutually unbiased basis,” Opt. Express 19, 3542 (2011).
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P. -A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113, 160401 (2014).
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H. Di Lorenzo Pires, C. H. Monken, and M. P. van Exter, “Direct measurement of transverse-mode entanglement in two-photon states,” Phys. Rev. A 80, 022307 (2009).
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Ding, Y.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285 (2018).
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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 (2000).
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Dudley, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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Eberly, J. H.

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
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M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, “Packet narrowing and quantum entanglement in photoionization and photodissociation,” Phys. Rev. A 69, 052117 (2004).
[Crossref]

Edgar, M.P.

M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
[Crossref]

Efremov, M. A.

M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, “Packet narrowing and quantum entanglement in photoionization and photodissociation,” Phys. Rev. A 69, 052117 (2004).
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Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
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Eisert, J.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt. 56, 1829–1837 (2009).
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J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
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A. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
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M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Phil. Trans. R. Soc. A 37520150442 (2017).
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F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional Bell basis,” Optica 4, 1462 (2017).
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Etcheverry, S.

D. Goyeneche, G. Cañas, S. Etcheverry, E. S. Gómez, G. B. Xavier, G. Lima, and A. Delgado, “Five measurement bases determine pure quantum states on any dimension,” Phys. Rev. Lett. 115, 090401 (2015).
[Crossref] [PubMed]

G. Cañas, S. Etcheverry, E. S. Gómez, C. Saavedra, G. B. Xavier, G. Lima, and A. Cabello, “Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem,” Phys. Rev. A 90, 012119 (2014).
[Crossref]

Faccio, D.

E. Bolduc, D. Faccio, and J. Leach, “Acquisition of multiple photon pairs with an EMCCD camera,” J. Opt. 19, 054006 (2017).
[Crossref]

Fedorov, M. V.

G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” EPL 87, 64003 (2009).
[Crossref]

M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, “Packet narrowing and quantum entanglement in photoionization and photodissociation,” Phys. Rev. A 69, 052117 (2004).
[Crossref]

Fernández, E.

Ferreira da Silva, T.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Fickler, R.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113, 13642 (2016).
[Crossref] [PubMed]

Figueroa, M.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. Ferreira da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Fonseca, E. J. S.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868 (1999).
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Forbes, A.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e150116 (2016).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Franke-Arnold, S.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
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M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
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Gatti, A.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[Crossref] [PubMed]

Genovese, M.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Phot. 4, 227–230 (2010).
[Crossref]

G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” EPL 87, 64003 (2009).
[Crossref]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722 (2000).
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S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploiting radiation pressure,” Phys. Rev. Lett. 88, 120401 (2002).
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Giovannini, D.

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Nat. Comm. (2)

M.P. Edgar, D.S. Tasca, F. Izdebski, R.E. Warburton, J. Leach, M. Agnew, G.S. Buller, R.W. Boyd, and M.J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Comm. 3, 984 (2012).
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Opt. Express (3)

Optica (1)

Phil. Trans. R. Soc. A (1)

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Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
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Phys. Rev. A (18)

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Figures (6)

Fig. 1
Fig. 1 Experimental setup. See the main text for more details.
Fig. 2
Fig. 2 Images recorded with the EMCCD camera for computing the initial Schmidt number K0. In (a) we show the near-field distribution generated by the transverse pump beam. In (b) we show the far-field distribution that arise from the phase-matching conditions. (c) and (d) show the corresponding fitting surfaces.
Fig. 3
Fig. 3 Numerical simulations for our entanglement distillation protocol. (a) The ratio K/K0 of the post-selected states when a and d are varying. (b) The success probability Psucc as function of a and d.
Fig. 4
Fig. 4 Some examples of the experimental results obtained for the first scenario considered, where d is fixed to 20 px and a is varying. In (a), (c) and (e) we show the recorded images at the near-field plane when a = 6, 8 and 14 px, respectively. (b), (d) and (f) show the corresponding recorded images at the far-field plane when a = 6, 8 and 14 px, respectively.
Fig. 5
Fig. 5 Some experimental results obtained for the second scenario considered, where d is varying. In (a), (c) and (e) we show the recorded images at the near-field plane when d =0, 14 and 19 px, respectively. In (b), (d) and (f) we show the corresponding recorded images at the far-field plane when d = 0, 14 and 19 px, respectively.
Fig. 6
Fig. 6 Experimental results for both scenarios considered for the entanglement distillation procedure. In (a) we show the recorded K values when d is fixed at 20 px while a is varying. In (b) we show the obtained K values when a is fixed at 7px and d is varying. Black dots correspond to the experimental results and the blue dashed line shows the initial value of the spatial entanglement K0. The pink area represents the confidence bound of K obtained by Monte-Carlo simulations and based on the experimental errors.

Tables (2)

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Table 1 Experimental results for K when d is fixed at 20 px while a is varying.

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Table 2 Experimental results for K when a is fixed at 7 px while d is varying.

Equations (12)

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| Ψ 12 = d q 1 d q 2 v ( q 1 + q 2 ) g ( q 1 q 2 ) | 1 q 1 | 1 q 2 .
| Ψ 12 = d x 1 d x 2 W ( x 1 + x 2 2 ) G ( x 1 x 2 2 ) | 1 x 1 | 1 x 2 ,
K = 1 4 π 2 [ d x j I ( x j ) ] 2 d x j I 2 ( x j ) × [ d q j I ( q j ) ] 2 d q j I 2 ( q j ) ,
I ( q j ) = d q i v 2 ( q i + q j ) g 2 ( q i q j ) , and
I ( x j ) = d x i W 2 ( x i + x j 2 ) G 2 ( x i x j 2 ) .
I ( q ) = g 2 ( 2 q ) sinc 2 ( L K | q | 2 ) , and
I ( x ) = W 2 ( x ) exp ( 2 | x | 2 σ 2 ) .
K = 3 π 2 σ 2 8 λ 3 L .
| Ψ 12 ( F ) = d x 1 d x 2 W ( x 1 + x 2 2 ) F ( x 1 ) F ( x 2 ) G ( x 1 x 2 2 ) | 1 x 1 | 1 x 2 .
F ( x ) = F ( x , y ) = [ e ( x d ) 2 4 a 2 + e ( x + d ) 2 4 a 2 ] [ e ( y d ) 2 4 a 2 + e ( y + d ) 2 4 a 2 ] .
I fit NF ( x , y ) = i = 1 4 α i exp ( ( x β i ) 2 δ i 2 ) exp ( ( y γ i ) 2 i 2 ) ,
I fit FF ( x , y ) = a + b sinc 2 ( c [ ( x x 0 ) 2 + ( y y 0 ) 2 ] ) .

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