Abstract

Multi-core optical fibers are readily used in endoscopic devices to transmit classical images. As an extension to the quantum domain, we study the transmission of the spatial quantum fluctuations of light through a conduit made of the ordered packing of thousands of fibers. Starting from twin beams that are correlated in their local intensity fluctuations, we show that, in the limit of a high density of constituent fiber cores, the intensity-difference squeezing present in arbitrary matching regions of the beams is preserved when one of the beams is sent through the conduit. The capability of using fiber bundles to transport quantum information encoded in the spatial degrees of freedom could bring guided-light technology to the emergent field of quantum imaging.

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2017 (4)

H. J. Lee, S-K Choi, and H. S. Park, “Experimental Demonstration of Four-Dimensional Photonic Spatial Entanglement between Multi-core Optical Fibres,” Sci. Rep. 7(1), 4302 (2017).
[Crossref] [PubMed]

Y. Israel, R. Tenne, D. Oron, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nature Communications 8(1), 14786 (2017).
[Crossref] [PubMed]

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

A. Perperidis, H. E. Parker, A. Karam-Eldaly, Y. Altmann, K. Dhaliwal, R. R. Thomson, M. G. Tanner, and S. McLaughlin, “Characterization and modelling of inter-core coupling in coherent fiber bundles,” Opt. Express 25(10), 11932–11953 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (1)

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of Localized Multi-Spatial-Mode Quadrature Squeezing,” Phys. Rev. X 5(3), 031004 (2015).

2014 (2)

V. Subramanian and Krish Ragunath, “Advanced Endoscopic Imaging: A Review of Commercially Available Technologies,” Clinical Gastroenterology and Hepatology,  12(3), 368–376 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J Knittel, B. Hage, H-A Bachor, and W. P. Bowen, “Subdiffraction-Limited Quantum Imaging within a Living Cell,” Phys. Rev. X 4(1), 011017 (2014).

2013 (3)

A. Fertman and D. Yelin, “Image transmission through an optical fiber using real-time modal phase restoration,” J. Opt. Soc. Am. B 30, (1)149–157 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
[Crossref]

E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S Olivares, G. Brida, and M. Genovese, “Experimental Realization of Quantum Illumination,” Phys. Rev. Lett. 110(15), 153603 (2013).
[Crossref] [PubMed]

2012 (2)

Y. Kang, J. Ko, S. M. Lee, S-K Choi, B. Y. Kim, and H. S. Park, “Measurement of the Entanglement between Photonic Spatial Modes in Optical Fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nature Communications 3(1), 1027 (2012).
[Crossref]

2011 (1)

W. Löffler, T. G. Euser, E. R. Eliel, M. Scharrer, P. St. J Russell, and J. P. Woerdman, “Fiber Transport of Spatially Entangled Photons,” Phys. Rev. Lett. 106(24), 240505 (2011).
[Crossref] [PubMed]

2010 (1)

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 4(1), 227–230 (2010).
[Crossref]

2009 (1)

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

2008 (2)

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of Spatially Broadband Twin Beams for Quantum Imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

2007 (1)

2004 (1)

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

2000 (1)

M. I. Kolobov and C. Fabre, “Quantum Limits on Optical Resolution,” Phys. Rev. Lett.,  85(18), 3789–3792 (2000).
[Crossref] [PubMed]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref] [PubMed]

1989 (1)

M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, (2)913–923 (1989).
[Crossref]

1987 (1)

Alleaume, R.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Altmann, Y.

Arimondo, E.

Bache, M.

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

Bachor, H-A

M. A. Taylor, J. Janousek, V. Daria, J Knittel, B. Hage, H-A Bachor, and W. P. Bowen, “Subdiffraction-Limited Quantum Imaging within a Living Cell,” Phys. Rev. X 4(1), 011017 (2014).

Bachor, H-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
[Crossref]

Barreiro, C.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Bouda, J.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Bowen, W. P.

M. A. Taylor, J. Janousek, V. Daria, J Knittel, B. Hage, H-A Bachor, and W. P. Bowen, “Subdiffraction-Limited Quantum Imaging within a Living Cell,” Phys. Rev. X 4(1), 011017 (2014).

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
[Crossref]

Boxleitner, W.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Boyer, V.

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of Localized Multi-Spatial-Mode Quadrature Squeezing,” Phys. Rev. X 5(3), 031004 (2015).

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of Spatially Broadband Twin Beams for Quantum Imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[Crossref]

Brambilla, E.

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

Brida, G.

E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S Olivares, G. Brida, and M. Genovese, “Experimental Realization of Quantum Illumination,” Phys. Rev. Lett. 110(15), 153603 (2013).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo-Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 4(1), 227–230 (2010).
[Crossref]

Caves, C.

Choi, S-K

H. J. Lee, S-K Choi, and H. S. Park, “Experimental Demonstration of Four-Dimensional Photonic Spatial Entanglement between Multi-core Optical Fibres,” Sci. Rep. 7(1), 4302 (2017).
[Crossref] [PubMed]

Y. Kang, J. Ko, S. M. Lee, S-K Choi, B. Y. Kim, and H. S. Park, “Measurement of the Entanglement between Photonic Spatial Modes in Optical Fibers,” Phys. Rev. Lett. 109(2), 020502 (2012).
[Crossref] [PubMed]

Cizmar, T.

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nature Communications 3(1), 1027 (2012).
[Crossref]

Crouch, D.

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J Knittel, B. Hage, H-A Bachor, and W. P. Bowen, “Subdiffraction-Limited Quantum Imaging within a Living Cell,” Phys. Rev. X 4(1), 011017 (2014).

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
[Crossref]

Debuisschert, T.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Degiovanni, I. P.

E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S Olivares, G. Brida, and M. Genovese, “Experimental Realization of Quantum Illumination,” Phys. Rev. Lett. 110(15), 153603 (2013).
[Crossref] [PubMed]

Dhaliwal, K.

Dholakia, K.

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nature Communications 3(1), 1027 (2012).
[Crossref]

Diamanti, E.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Dianati, M.

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M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
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M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
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A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
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Querasser, E.

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Rigneault, H.

Robyr, S.

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Ruo Berchera, I.

E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S Olivares, G. Brida, and M. Genovese, “Experimental Realization of Quantum Illumination,” Phys. Rev. Lett. 110(15), 153603 (2013).
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Salvail, L.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Scharrer, M.

W. Löffler, T. G. Euser, E. R. Eliel, M. Scharrer, P. St. J Russell, and J. P. Woerdman, “Fiber Transport of Spatially Entangled Photons,” Phys. Rev. Lett. 106(24), 240505 (2011).
[Crossref] [PubMed]

Sharpe, A. W.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Shields, A. J.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Silberberg, Y.

Y. Israel, R. Tenne, D. Oron, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nature Communications 8(1), 14786 (2017).
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Stucki, D.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Subramanian, V.

V. Subramanian and Krish Ragunath, “Advanced Endoscopic Imaging: A Review of Commercially Available Technologies,” Clinical Gastroenterology and Hepatology,  12(3), 368–376 (2014).
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Suda, M.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Tamas, C.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Tanner, M. G.

Taylor, M. A.

M. A. Taylor, J. Janousek, V. Daria, J Knittel, B. Hage, H-A Bachor, and W. P. Bowen, “Subdiffraction-Limited Quantum Imaging within a Living Cell,” Phys. Rev. X 4(1), 011017 (2014).

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H-A. Bachor, and W. P. Bowen, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 7(1), 229–233 (2013).
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Tenne, R.

Y. Israel, R. Tenne, D. Oron, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nature Communications 8(1), 14786 (2017).
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Themel, T.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Thew, R. T.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Thoma, Y.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Thomson, R. R.

Treiber, A.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Trinkler, P.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Tualle-Brouri, R.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Turnbull, M. T.

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Vannel, F.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Walenta, N.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
[Crossref]

Weier, H.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Weinfurter, H.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Wimberger, I.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Woerdman, J. P.

W. Löffler, T. G. Euser, E. R. Eliel, M. Scharrer, P. St. J Russell, and J. P. Woerdman, “Fiber Transport of Spatially Entangled Photons,” Phys. Rev. Lett. 106(24), 240505 (2011).
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Yuan, Z. L.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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Zbinden, H.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Furst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hubel, G. Humer, T. Langer, M. Legre, R. Lieger, J. Lodewyck, T. Lorunser, N. Lutkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New. J. Phys,  11(2), 075001 (2009).
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This a transverse coherence length and the only one we will refer to in the rest of the paper.

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Figures (4)

Fig. 1
Fig. 1 Experimental setup. The conjugate and probe beams are generated via 4WM in the 85Rb cell. The probe light in the object plane, i.e. the plane at the position of the cell, where the correlations are created, is imaged onto the input face of the conduit. The probe light emerging from the output face of the conduit is imaged onto the probe slit on the measurement plane (Mp) using a high numerical aperture optical system. The conjugate is directly imaged onto the conjugate slit on the measurement plane (Mc). The conjugate slit is translated in horizontal (H) and vertical (V) directions perpendicular to the direction of propagation k, for every position of the probe slit as shown in the inset. The polarizing beamsplitter (PBS) and the half-wave plate (HWP) in the path of the conjugate provide a tunable loss for the channel to balance the beams intensities in the case where the probe is sent through the conduit. The lightly colored paths depict the geometric propagation of the quantum fluctuations whereas the densely colored paths depict the Gaussian propagation of the bright probe and conjugate beams. The pump beam is not shown for clarity. The figures of eight indicate CV entanglement (solid line) and quantum intensity correlations (dashed line).
Fig. 2
Fig. 2 Images of the probe beam after the conduit. a,b Images of the near- and far-field beam patterns after the conduit, showing the Gaussian intensity envelope. c,d Selected magnified regions across the profiles in a and b, respectively. In c, in the near-field, the characteristic pattern coming from the hexagonal lattice of constituent fibers can be clearly seen at the output face of the conduit. The lattice spacing is about 12 μm. Since the fibers are multimode, the emerging mode shape is random across the fiber lattice. The enclosed circular area represents the estimated coherence area of the process. In d, in the far field the fiber lattice pattern is transformed into a speckle pattern as the light from every fiber acquires a random phase.
Fig. 3
Fig. 3 Scanning noise data relative to shot noise. The measurement procedure is done by scanning the slit position on the conjugate beam for fixed positions of the slit on the probe beam. The result is a single dip in the detected noise for each scan. The scanning is done in both horizontal a,b and vertical c,d directions for the cases where the conduit is inserted in the probe beam path in a,c, and when it is not present b,d. The top graph in each figure is the fitted intensity profile of the conjugate beam. The noise dips are fitted using Gaussians and the black solid line at 0 dB represents the shot noise. The bar in each beam profile graph denotes the slit size. The excess amplification noise, observed when the slits positions do not match, is larger at the center of the gain medium, where the Gaussian pump beam profile peaks and the gain is the largest. The intensity profile of the conjugate beam is given in arbitrary units (a.u.). No electronic noise or other technical noise have been subtracted from the data.
Fig. 4
Fig. 4 Theoretical model of losses in the experiment. a. The FWM medium has a gain of G. The input probe and conjugate annihilation operators are depicted by a ^ and b ^. After the amplification the operators are a ^ and b ^ and after mixing vacuum fields c ^ and d ^ at beamsplitters with transmission Ta and Tb the operators are transformed to a ^ and b ^ . b. Optimization of conjugate transmission. The probe transmission is 0.3 and the maximum squeezing for a gain of 1.5 can be seen to happen at transmission of the conjugate of 0.75. The solid black line is the shot noise.

Equations (4)

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a ^ = G T a a ^ ( G 1 ) T a b ^ + 1 T a c ^ b ^ = ( G 1 ) T b a ^ + G T b b ^ + 1 T b d ^ ,
( Δ n ^ ) 2 = { [ G T a T b ( G 1 ) ] 2 + G ( G 1 ) ( T b T a ) 2 + G T a ( 1 T a ) + ( G 1 ) T b ( 1 T b ) } | α | 2 .
n ^ + = [ G T a + ( G 1 ) T b ] | α | 2 .
( Δ n ^ ) 2 n ^ + .

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