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Entanglement of the orbital angular momentum states of photons


Entangled quantum states are not separable, regardless of the spatial separation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum non-locality1,2. An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement. Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems3,4,5,6, involving, for example, the two orthogonal polarization states of photons. Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum. As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information7,8, enabling, for example, more efficient use of communication channels in quantum cryptography9,10,11.

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Figure 1: The wave front (top) and the intensity pattern (bottom) of the simplest Laguerre–gaussian (LGlp) or ‘doughnut’ mode.
Figure 2: Experimental set-up for single-photon mode detection.
Figure 3: Conservation of orbital angular momentum.
Figure 4: Experimental evidence (left; right, simulation) of entanglement of photon states with phase singularities.


  1. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812; 823–828; 844–849 (1935).

    Article  Google Scholar 

  2. Schrödinger, E. Discussion of probability relations between separated systems. Proc. Camb. Phil. Soc. 31, 555–563 (1935).

    Article  Google Scholar 

  3. Bouwmeester, D., Pan, J.-W., Daniell, M., Weinfurter, H. & Zeilinger, A. Observation of a three-photon Greenberger-Horne-Zeilinger state. Phys. Rev. Lett. 82, 1345–1349 (1999).

    MathSciNet  CAS  Article  Google Scholar 

  4. Pan, J.-W., Bouwmeester, D., Daniell, M., Weinfurter, H. & Zeilinger, A. Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement. Nature 403, 515–519 (2000).

    CAS  Article  Google Scholar 

  5. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000).

    CAS  Article  Google Scholar 

  6. Pan, J.-W., Daniell, M., Gasparoni, S., Weihs, G. & Zeilinger, A. Experimental demonstration of four-photon entanglement and high-fidelity teleportation. Phys. Rev. Lett. 86, 4435–4438 (2001).

    CAS  Article  Google Scholar 

  7. DiVincenzo, D. P., More, T., Shor, P. W., Smolin, J. A. & Terhal, B. M. Unextendible product bases, uncompletable product bases and bound entanglement. Preprint quant-ph/9908070 at 〈〉 (1999).

  8. Bartlett, S. D., de Guise, H. & Sanders, B. C. Quantum computation with harmonic oscillators. Preprint quant-ph/0011080 at 〈〉 (2000).

  9. Bechmann-Pasquinucci, H. & Peres, A. Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85, 3313–3316 (2000).

    MathSciNet  CAS  Article  Google Scholar 

  10. Bechmann-Pasquinucci, H. & Tittel, W. Quantum cryptography using larger alphabets. Phys. Rev. A 61, 62308–62313 (2000).

    MathSciNet  Article  Google Scholar 

  11. Bourennane, M., Karlsson, A. & Björk, G. Quantum key distribution using multilevel encoding. Phys. Rev. A (in the press).

  12. Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).

    CAS  Article  Google Scholar 

  13. Zukowski, M., Zeilinger, A. & Horne, M. Realizable higher-dimensional two-particle entanglements via multiport beam splitters. Phys. Rev. A 55, 2564–2579 (1997).

    CAS  Article  Google Scholar 

  14. Reck, M. Quantum Interferometry with Multiports: Entangled Photons in Optical Fibers. Thesis, Univ. Innsbruck (1996).

    Google Scholar 

  15. Arnaut, H. H. & Barbosa, G. A. Orbital and angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion. Phys. Rev. Lett. 85, 286–289 (2000).

    CAS  Article  Google Scholar 

  16. Franke-Arnold, S., Barnett, S. M., Padgett, M. J. & Allen, L. Two-photon entanglement of orbital angular momentum states. Phys. Rev. A (in the press).

  17. 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).

    CAS  Article  Google Scholar 

  18. He, H., Fries, M., Heckenberg, N. & Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorbtive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 75, 826–829 (1995).

    CAS  Article  Google Scholar 

  19. Simpson, N. B., Dholakia, K., Allen, L. & Padgett, M. J. Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner. Opt. Lett. 22, 52–54 (1997).

    CAS  Article  Google Scholar 

  20. Galajda, P. & Ormos, P. Complex micromachines produced and driven by light. Appl. Phys. Lett. 78, 249–251 (2001).

    CAS  Article  Google Scholar 

  21. Friese, M. E. J., Enger, J., Rubinsztein-Dunlop, H. & Heckenberg, N. Optical angular-momentum transfer to trapped absorbing particles. Phys. Rev. A 54, 1593–1596 (1996).

    CAS  Article  Google Scholar 

  22. Bejersbergen, M. W., Allen, L., van der Veen, H. E. L. O. & Woerdman, J. P. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 96, 123–132 (1993).

    Article  Google Scholar 

  23. Arlt, J., Dholakia, K., Allen, L. & Padgett, M. J. The production of multiringed laguerre-gaussian modes by computer-generated holograms. J. Mod. Opt. 45, 1231–1237 (1998).

    CAS  Article  Google Scholar 

  24. Arlt, J., Dholakia, K., Allen, L. & Padgett, M. Parametric down-conversion for light beams possessing orbital angular momentum. Phys. Rev. A 59, 3950–3952 (1999).

    CAS  Article  Google Scholar 

  25. Kaszlikowski, D., Gnacinski, P., Zukowski, M., Miklaszewski, W. & Zeilinger, A. Violation of local realism by two entangled n-dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85, 4418–4421 (2000).

    CAS  Article  Google Scholar 

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This work was supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF).

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Correspondence to Anton Zeilinger.

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

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