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Characterizing quantum channels with non-separable states of classical light

Nature Physics volume 13, pages 397–402 (2017)Cite this article

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Abstract

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

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Figure 1: Illustration of the concept.
Figure 2: Experimental set-up.
Figure 3: Evolution of classical entanglement in turbulence.
Figure 4: Evolution of the mode spectrum in turbulence.
Figure 5: Experimental results for data transmission over turbulent channel.

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  • 31 March 2017

    In the version of this Article originally published, a credit line was missing for the image of Maxwell in Fig. 5. It should have read: 'Maxwell image credit: Bettmann / Contributor/ Bettmann / Getty Images.'

References

  1. Ursin, R. et al. Entanglement-based quantum communication over 144 km. Nat. Phys. 3, 481–486 (2007).

    Google Scholar 

  2. Ma, X.-S. et al. Quantum teleportation over 143 kilometres using active feed-forward. Nature 489, 269–273 (2012).

    ADS  Google Scholar 

  3. Yin, J. et al. Quantum teleportation and entanglement distribution over 100-kilometre free-space channels. Nature 488, 185–188 (2012).

    ADS  Google Scholar 

  4. Herbst, T. et al. Teleportation of entanglement over 143 km. Proc. Natl Acad. Sci. USA 112, 14202–14205 (2015).

    ADS  Google Scholar 

  5. Cerf, N. J., Bourennane, M., Karlsson, A. & Gisin, N. Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

  8. Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nat. Commun. 5, 4502 (2014).

    ADS  Google Scholar 

  9. Zhang, Y. et al. Engineering two-photon high-dimensional states through quantum interference. Sci. Adv. 2, e1501165 (2016).

    ADS  Google Scholar 

  10. Forbes, A., Dudley, A. & McLaren, M. Creation and detection of optical modes with spatial light modulators. Adv. Opt. Photon. 8, 200–227 (2016).

    Google Scholar 

  11. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    ADS  Google Scholar 

  12. Malik, M. et al. Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding. Opt. Express 20, 13195–13200 (2012).

    ADS  Google Scholar 

  13. Rodenburg, B. et al. Influence of atmospheric turbulence on states of light carrying orbital angular momentum. Opt. Lett. 37, 3735–3737 (2012).

    ADS  Google Scholar 

  14. Paterson, C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Phys. Rev. Lett. 94, 153901 (2005).

    ADS  Google Scholar 

  15. Gopaul, C. & Andrews, R. The effect of atmospheric turbulence on entangled orbital angular momentum states. New J. Phys. 9, 94 (2007).

    ADS  Google Scholar 

  16. Tyler, G. A. & Boyd, R. W. Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum. Opt. Lett. 34, 142–144 (2009).

    ADS  Google Scholar 

  17. Chen, C., Yang, H., Tong, S. & Lou, Y. Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence. Opt. Express 24, 6959–6975 (2016).

    ADS  Google Scholar 

  18. Neo, R. et al. Measurement and limitations of optical orbital angular momentum through corrected atmospheric turbulence. Opt. Express 24, 2919–2930 (2016).

    ADS  Google Scholar 

  19. Roux, F. S., Wellens, T. & Shatokhin, V. N. Entanglement evolution of twisted photons in strong atmospheric turbulence. Phys. Rev. A 92, 012326 (2015).

    ADS  Google Scholar 

  20. Ibrahim, A. H., Roux, F. S., McLaren, M., Konrad, T. & Forbes, A. Orbital-angular-momentum entanglement in turbulence. Phys. Rev. A 88, 012312 (2013).

    ADS  Google Scholar 

  21. Souza, C. et al. Quantum key distribution without a shared reference frame. Phys. Rev. A 77, 032345 (2008).

    ADS  MathSciNet  MATH  Google Scholar 

  22. D’Ambrosio, V. et al. Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 3, 961 (2012).

    ADS  Google Scholar 

  23. Vallone, G. et al. Free-space quantum key distribution by rotation-invariant twisted photons. Phys. Rev. Lett. 113, 060503 (2014).

    ADS  Google Scholar 

  24. Farías, O. J. et al. Resilience of hybrid optical angular momentum qubits to turbulence. Sci. Rep. 5, 8424 (2015).

    Google Scholar 

  25. Krenn, M., Handsteiner, J., Fink, M., Fickler, R. & Zeilinger, A. Twisted photon entanglement through turbulent air across Vienna. Proc. Natl Acad. Sci. USA 112, 14197–14201 (2015).

    ADS  Google Scholar 

  26. Löffler, W. et al. Fiber transport of spatially entangled photons. Phys. Rev. Lett. 106, 240505 (2011).

    ADS  Google Scholar 

  27. Kang, Y. et al. Measurement of the entanglement between photonic spatial modes in optical fibers. Phys. Rev. Lett. 109, 020502 (2012).

    ADS  Google Scholar 

  28. Mohseni, M., Rezakhani, A. T. & Lidar, D. A. Quantum-process tomography: resource analysis of different strategies. Phys. Rev. A 77, 032322 (2008).

    ADS  Google Scholar 

  29. Bromberg, Y., Lahini, A., Morandotti, F. & Silberberg, Y. Quantum and classical correlations in waveguide lattices. Phys. Rev. Lett. 102, 253904 (2009).

    ADS  Google Scholar 

  30. Keil, R. et al. Photon correlations in two-dimensional waveguide arrays and their classical estimate. Phys. Rev. A 81, 023834 (2010).

    ADS  Google Scholar 

  31. Keil, R. et al. Classical characterization of biphoton correlation in waveguide lattices. Phys. Rev. A 83, 013808 (2011).

    ADS  Google Scholar 

  32. Spreeuw, R. J. C. A classical analogy of entanglement. Found. Phys. 28, 361 (1998).

    MathSciNet  Google Scholar 

  33. Pereira, L. J., Khoury, A. Z. & Dechoum, K. Quantum and classical separability of spin–orbit laser modes. Phys. Rev. A 90, 053842 (2014).

    ADS  Google Scholar 

  34. Töppel, F., Aiello, A., Marquardt, C., Giacobino, E. & Leuchs, G. Classical entanglement in polarization metrology. New. J. Phys. 16, 073019 (2014).

    ADS  Google Scholar 

  35. Guzman-Silva, D. et al. Demonstration of local teleportation using classical entanglement. Laser Photon. Rev. 10, 317–321 (2016).

    ADS  Google Scholar 

  36. Karimi, E. & Boyd, R. W. Classical entanglement? Science 350, 1172–1173 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  37. D’Ambrosio, V. et al. Photonic polarization gears for ultra-sensitive angular measurements. Nat. Commun. 4, 2432 (2013).

    ADS  Google Scholar 

  38. Karimi, E. et al. Spin–orbit hybrid entanglement of photons and quantum contextuality. Phys. Rev. A 82, 022115 (2010).

    ADS  Google Scholar 

  39. Jiang, M., Luo, S. & Fu, S. Channel-state duality. Phys. Rev. A 87, 022310 (2013).

    ADS  Google Scholar 

  40. Dür, W., Hein, M., Cirac, J. I. & Briegel, H. J. Standard forms of noisy quantum operations via depolarization. Phys. Rev. A 72, 052326 (2005).

    ADS  Google Scholar 

  41. Milione, G., Sztul, H., Nolan, D. & Alfano, R. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).

    ADS  Google Scholar 

  42. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    ADS  Google Scholar 

  43. Wootters, W. Entanglement of formation and concurrence. Quant. Inf. Comput. 1, 27–44 (2001).

    MathSciNet  MATH  Google Scholar 

  44. McLaren, M., Konrad, T. & Forbes, A. Measuring the nonseparability of vector vortex beams. Phys. Rev. A 92, 023833 (2015).

    ADS  Google Scholar 

  45. Konrad, T. et al. Evolution equation for quantum entanglement. Nat. Phys. 4, 99–102 (2008).

    Google Scholar 

  46. Milione, G., Nguyen, T. A., Leach, J., Nolan, D. A. & Alfano, R. R. Using the nonseparability of vector beams to encode information for optical communication. Opt. Lett. 40, 4887–4890 (2015).

    ADS  Google Scholar 

  47. Naidoo, D. et al. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat. Photon. 10, 327–332 (2016).

    ADS  Google Scholar 

  48. Marrucci, L., Manzo, C. & Papro, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).

    ADS  Google Scholar 

  49. Jack, B., Leach, J., Ritsch, H., Barnett, S. & Padgett, M. Precise quantum tomography of photon pairs with entangled orbital angular momentum. New J. Phys. 811, 103024 (2009).

    Google Scholar 

  50. Andrews, L. C. & Phillips, R. L. Laser Beam Propagation through Random Media (SPIE Press, 1998).

    Google Scholar 

  51. Fried, D. L. Optical resolution through a randomly inhomogeneous medium for very long and very short exposures. J. Opt. Soc. Am. 56, 1372–1379 (1966).

    ADS  Google Scholar 

  52. Leader, J. C. Atmospheric propagation of partially coherent radiation. J. Opt. Soc. Am. 68, 175–185 (1978).

    ADS  Google Scholar 

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Acknowledgements

We express our gratitude to L. Marrucci for providing us with q-plates. B.N. acknowledges financial support from the National Research Foundation of South Africa and the African Laser Centre. C.R.-G. acknowledges Claude Leon Foundation. B.P.-G., C.R.-G. and R.I.H.-A. acknowledge support from CONACyT.

Author information

Author notes

  1. Yingwen Zhang

    Present address: Present address: Physics Department, Centre for Research in Photonics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada.,

Authors and Affiliations

  1. School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa

    Bienvenu Ndagano, Benjamin Perez-Garcia, Filippus S. Roux, Melanie McLaren, Carmelo Rosales-Guzman, Othmane Mouane & Andrew Forbes

  2. Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849, Mexico

    Benjamin Perez-Garcia & Raul I. Hernandez-Aranda

  3. National Metrology Institute of South Africa, Meiring Naude Road, Pretoria, South Africa

    Filippus S. Roux

  4. CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa

    Yingwen Zhang

  5. School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa

    Thomas Konrad

Authors
  1. Bienvenu Ndagano
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Contributions

The conceptual idea was formulated by A.F. and T.K. The theoretical formalism was laid out by A.F., T.K., F.S.R., B.N. and B.P.-G. The classical experiments were carried out by B.N., B.P.-G., O.M. and C.R.-G., while the quantum experiment was carried out by Y.Z. All authors contributed to the data analysis and interpretation of the results. B.N. wrote the manuscript with inputs from all the authors. A.F. supervised the project.

Corresponding author

Correspondence to Andrew Forbes.

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The authors declare no competing financial interests.

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Ndagano, B., Perez-Garcia, B., Roux, F. et al. Characterizing quantum channels with non-separable states of classical light. Nature Phys 13, 397–402 (2017). https://doi.org/10.1038/nphys4003

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