Abstract

High-dimensional entanglement has demonstrated its potential for increasing channel capacity and resistance to noise in quantum information processing. However, distributing it is a challenging task, imposing severe restrictions on its application. Here we report the first distribution of three-dimensional orbital angular momentum (OAM) entanglement via a 1-km-long few-mode optical fiber. Using an actively stabilizing phase precompensation technique, we successfully transport one photon of a three-dimensional OAM entangled photon pair through the fiber. The distributed OAM entangled state still shows a fidelity up to 71% with respect to the three-dimensional maximally entangled state (MES). In addition, we certify that the high-dimensional quantum entanglement survives the transportation by violating a generalized Bell inequality, obtaining a violation of $ \sim 3 $ standard deviations from the classical limit with $ {I_3} = 2.12 \pm 0.04 $. The method we developed can be extended to a higher OAM dimension and larger distances in principle. Our results make a significant step towards future OAM-based high-dimensional long-distance quantum communication.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2020 (1)

J. Liu, I. Nape, Q. Wang, A. Vallés, J. Wang, and A. Forbes, “Multidimensional entanglement transport through single-mode fiber,” Sci. Adv. 6, eaay0837 (2020).
[Crossref]

2019 (5)

D. Cozzolino, E. Polino, M. Valeri, G. Carvacho, D. Bacco, N. Spagnolo, L. K. Oxenløwe, and F. Sciarrino, “Air-core fiber distribution of hybrid vector vortex-polarization entangled states,” Adv. Photon. 1, 046005 (2019).
[Crossref]

L.-J. Kong, R. Liu, Z.-X. Wang, W.-R. Qi, S.-Y. Huang, Q. Wang, C. Tu, Y. Li, and H.-T. Wang, “Manipulation of eight-dimensional Bell-like states,” Sci. Adv. 5, eeat9206 (2019).
[Crossref]

D. Cozzolino, D. Bacco, B. Da Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenløwe, “Orbital angular momentum states enabling fiber-based high-dimensional quantum communication,” Phys. Rev. Appl. 11, 064058 (2019).
[Crossref]

Y.-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y. Lu, A. Zeilinger, and J.-W. Pan, “Quantum teleportation in high dimensions,” Phys. Rev. Lett. 123, 070505 (2019).
[Crossref]

S. Ecker, F. Bouchard, L. Bulla, F. Brandt, O. Kohout, F. Steinlechner, R. Fickler, M. Malik, Y. Guryanova, R. Ursin, and M. Huber, “Overcoming noise in entanglement distribution,” Phys. Rev. X 9, 041042 (2019).
[Crossref]

2018 (3)

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26, 31925–31941 (2018).
[Crossref]

T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep. 8, 817 (2018).
[Crossref]

X.-M. Hu, B.-H. Liu, Y. Guo, G.-Y. Xiang, Y.-F. Huang, C.-F. Li, G.-C. Guo, M. Kleinmann, T. Vértesi, and A. Cabello, “Observation of stronger-than-binary correlations with entangled photonic qutrits,” Phys. Rev. Lett. 120, 180402 (2018).
[Crossref]

2017 (5)

F. Steinlechner, S. Ecker, M. Fink, B. Liu, J. Bavaresco, M. Huber, T. Scheidl, and R. Ursin, “Distribution of high-dimensional entanglement via an intra-city free-space link,” Nat. Commun. 8, 15971 (2017).
[Crossref]

H. J. Lee, S.-K. Choi, and H. S. Park, “Experimental demonstration of four-dimensional photonic spatial entanglement between multi-core optical fibers,” Sci. Rep. 7, 4302 (2017).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
[Crossref]

F. Wang, M. Erhard, A. Babazadeh, M. Malik, M. Krenn, and A. Zeilinger, “Generation of the complete four-dimensional Bell basis,” Optica 4, 1462–1467 (2017).
[Crossref]

2016 (3)

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. USA 113, 13642–13647 (2016).
[Crossref]

M. Kleinmann and A. Cabello, “Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements,” Phys. Rev. Lett. 117, 150401 (2016).
[Crossref]

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nat. Photonics 10, 248–252 (2016).
[Crossref]

2015 (3)

T. M. Graham, H. J. Bernstein, T.-C. Wei, M. Junge, and P. G. Kwiat, “Superdense teleportation using hyperentangled photons,” Nat. Commun. 6, 7185 (2015).
[Crossref]

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, and A. Zeilinger, “Twisted photon entanglement through turbulent air across Vienna,” Proc. Natl. Acad. Sci. USA 112, 14197–14201 (2015).
[Crossref]

Z.-Q. Zhou, Y.-L. Hua, X. Liu, G. Chen, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, “Quantum storage of three-dimensional orbital-angular-momentum entanglement in a crystal,” Phys. Rev. Lett. 115, 070502 (2015).
[Crossref]

2014 (4)

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, “Limitations to the determination of a Laguerre–Gauss spectrum via projective, phase-flattening measurement,” J. Opt. Soc. Am. B 31, A20–A23 (2014).
[Crossref]

W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
[Crossref]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. USA 111, 6243–6247 (2014).
[Crossref]

2013 (5)

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

J. Nunn, L. Wright, C. Söller, L. Zhang, I. Walmsley, and B. Smith, “Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion,” Opt. Express 21, 15959–15973 (2013).
[Crossref]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
[Crossref]

J. Capenter, C. Xiong, M. J. Collins, J. Li, T. F. Krauss, and B. J. Eggleton, “Mode multiplexed single-photon and classical channels in a few-mode fiber,” Opt. Express 21, 28794–28800 (2013).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

2012 (5)

F. Miatto, D. Giovannini, J. Romero, S. Franke-Arnold, S. Barnett, and M. Padgett, “Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems,” Eur. Phys. J. D 66, 1–6 (2012).
[Crossref]

F. M. Miatto, H. D. L. Pires, S. M. Barnett, and M. P. van Exter, “Spatial Schmidt modes generated in parametric down-conversion,” Eur. Phys. J. D 66, 263 (2012).
[Crossref]

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, 020502 (2012).
[Crossref]

V. D’Ambrosio, E. Nagali, S. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

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

2011 (3)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

W. Löffler, T. Euser, E. Eliel, M. Scharrer, P. St. J. Russell, and J. Woerdman, “Fiber transport of spatially entangled photons,” Phys. Rev. Lett. 106, 240505 (2011).
[Crossref]

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[Crossref]

2007 (2)

L. Aolita and S. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98, 100501 (2007).
[Crossref]

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref]

2005 (1)

P. Hyllus, O. Gühne, D. Bruß, and M. Lewenstein, “Relations between entanglement witnesses and Bell inequalities,” Phys. Rev. A 72, 012321 (2005).
[Crossref]

2004 (1)

N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Measuring entangled qutrits and their use for quantum bit commitment,” Phys. Rev. Lett. 93, 053601 (2004).
[Crossref]

2003 (3)

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[Crossref]

J. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[Crossref]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
[Crossref]

2002 (4)

R. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66, 012303 (2002).
[Crossref]

A. O’neil, I. MacVicar, L. Allen, and M. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref]

2000 (1)

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

Alexandrescu, A.

J. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[Crossref]

Ali-Khan, I.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref]

Allen, L.

A. O’neil, I. MacVicar, L. Allen, and M. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

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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, 1462–1467 (2017).
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A. Babazadeh, M. Erhard, F. Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, “High-dimensional single-photon quantum gates: concepts and experiments,” Phys. Rev. Lett. 119, 180510 (2017).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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Y.-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y. Lu, A. Zeilinger, and J.-W. Pan, “Quantum teleportation in high dimensions,” Phys. Rev. Lett. 123, 070505 (2019).
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W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
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Z.-Q. Zhou, Y.-L. Hua, X. Liu, G. Chen, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, “Quantum storage of three-dimensional orbital-angular-momentum entanglement in a crystal,” Phys. Rev. Lett. 115, 070502 (2015).
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Adv. Photon. (1)

D. Cozzolino, E. Polino, M. Valeri, G. Carvacho, D. Bacco, N. Spagnolo, L. K. Oxenløwe, and F. Sciarrino, “Air-core fiber distribution of hybrid vector vortex-polarization entangled states,” Adv. Photon. 1, 046005 (2019).
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Eur. Phys. J. D (2)

F. Miatto, D. Giovannini, J. Romero, S. Franke-Arnold, S. Barnett, and M. Padgett, “Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems,” Eur. Phys. J. D 66, 1–6 (2012).
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F. M. Miatto, H. D. L. Pires, S. M. Barnett, and M. P. van Exter, “Spatial Schmidt modes generated in parametric down-conversion,” Eur. Phys. J. D 66, 263 (2012).
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J. Opt. Soc. Am. B (1)

Nat. Commun. (5)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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R. Fickler, R. Lapkiewicz, M. Huber, M. P. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
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F. Steinlechner, S. Ecker, M. Fink, B. Liu, J. Bavaresco, M. Huber, T. Scheidl, and R. Ursin, “Distribution of high-dimensional entanglement via an intra-city free-space link,” Nat. Commun. 8, 15971 (2017).
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V. D’Ambrosio, E. Nagali, S. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

T. M. Graham, H. J. Bernstein, T.-C. Wei, M. Junge, and P. G. Kwiat, “Superdense teleportation using hyperentangled photons,” Nat. Commun. 6, 7185 (2015).
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Nat. Photonics (1)

M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nat. Photonics 10, 248–252 (2016).
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Nat. Phys. (1)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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Nature (1)

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Opt. Express (3)

Optica (1)

Phys. Rev. A (8)

J. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
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P. Hyllus, O. Gühne, D. Bruß, and M. Lewenstein, “Relations between entanglement witnesses and Bell inequalities,” Phys. Rev. A 72, 012321 (2005).
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F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
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R. Thew, K. Nemoto, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66, 012303 (2002).
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J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, “Preparation of engineered two-photon entangled states for multidimensional quantum information,” Phys. Rev. A 67, 052313 (2003).
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J. Romero, D. Giovannini, S. Franke-Arnold, S. Barnett, and M. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
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H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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Phys. Rev. Appl. (1)

D. Cozzolino, D. Bacco, B. Da Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenløwe, “Orbital angular momentum states enabling fiber-based high-dimensional quantum communication,” Phys. Rev. Appl. 11, 064058 (2019).
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Phys. Rev. Lett. (15)

Z.-Q. Zhou, Y.-L. Hua, X. Liu, G. Chen, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, “Quantum storage of three-dimensional orbital-angular-momentum entanglement in a crystal,” Phys. Rev. Lett. 115, 070502 (2015).
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W. Zhang, Q. Qi, J. Zhou, and L. Chen, “Mimicking Faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112, 153601 (2014).
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M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
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Supplementary Material (1)

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» Supplement 1       Supplementary Material

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Figures (3)

Fig. 1.
Fig. 1. Schematic of the experimental setup. The entangled photons are generated by Type-II SPDC in a PPKTP crystal. The idler photon is directly measured (Alice) while the signal photon is fed to a precompensation module and coupled into a 1-km-long few-mode fiber and finally analyzed (Bob). The single photon detectors we used are InGaAs detectors. Here the dotted box is an actively locked unbalanced MZ interferometer (more details are shown in the inset). Both the 1550 nm single photon and classical 775 nm reference beam go through the Mach–Zehnder interferometer.
Fig. 2.
Fig. 2. Reconstructed density matrices (a), (b) before and (c), (d) after distribution. The real parts of the reconstructed density matrix are shown in (a) and (c), and the imaginary parts are shown in (b) and (d). For comparison, the closest maximally entangled state (MES) and the difference of the density matrix elements between the experimental result and theoretical MES are shown together in the orange-outlined insets.
Fig. 3.
Fig. 3. Intermodal dispersion. The normalized coincidence rate is the ratio between each measured coincidence rate and their sum. The horizontal coordinate represents the optical delay between the signal and idler photons. The blue dots represent the coincidence rates for of $ | {0,0} \rangle $ and the orange dots are for $ | { - 1,1}\rangle $. The intermodal dispersion is estimated by taking the difference in time of the peaks of the Gaussian fits (solid line).

Equations (6)

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| Ψ S P D C = , p s , p i C , p s , p i | , p s | , p i ,
| Ψ S P D C = C 0 , 0 | 0 | 0 + C 1 , 1 | 1 | 1 + C 1 , 1 | 1 | 1 .
| Ψ M E S ( θ , φ ) = ( e i θ | 1 | 1 + | 0 | 0 + e i φ | 1 | 1 ) / 3 ,
| Ψ M E S ( θ , φ ) = ( e i θ | 1 | 1 + | 0 | 0 + e i φ | 1 | 1 ) / 3 ,
I 3 + [ P ( A 1 = B 1 ) + P ( B 1 = A 2 + 1 ) + P ( A 2 = B 2 ) + P ( B 2 = A 1 ) ] [ P ( A 1 = B 1 1 ) + P ( B 1 = A 2 ) + P ( A 2 = B 2 1 ) + P ( B 2 = A 1 1 ) ] ,
P ( A a = B b + k ) j = 0 2 P ( A a = j , B b = j + k m o d 2 ) .

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