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Abstract

Quantum superposition is the quantum-mechanical property of a particle whereby it inhabits several of its possible quantum states simultaneously. Ideally, this permissible coexistence of quantum states, as defined on any degree of freedom, whether spin, frequency or spatial, can be used to fully exploit the information capacity of the associated physical system. In quantum optics, single photons are the quanta of light, and their coherence properties allow them to establish entangled superpositions between a large number of channels, making them favourable for realizations of quantum information processing schemes. In particular, single-photon W-states (that is, states exhibiting a uniform distribution of the photons across multiple modes) represent a class of multipartite maximally-entangled quantum states that are highly robust to dissipation. Here, we report on the generation and verification of single-photon W-states involving up to 16 spatial modes, and exploit their underlying multi-mode superposition for the on-chip generation of genuine random numbers.

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Change history

  • 18 September 2014

    In the version of this Article originally published, the contribution of Demetrios N. Christodoulides to conceiving the idea behind the work was not acknowledged in the Author Contributions section. This error has now been corrected in the HTML and PDF versions of the Article.

References

  1. 1.

    , , & Entanglement polytopes: multiparticle entanglement from single-particle information. Science 340, 1205–1208 (2013).

  2. 2.

    , & High-NOON states by mixing quantum and classical light. Science 328, 879–881 (2010).

  3. 3.

    et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010).

  4. 4.

    , , & Multiparticle entanglement. Found. Phys. 29, 527–552 (1999).

  5. 5.

    , & Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).

  6. 6.

    et al. Scalable multiparticle entanglement of trapped ions. Nature 438, 643–646 (2005).

  7. 7.

    et al. Witnessing trustworthy single-photon entanglement with local homodyne measurements. Phys. Rev. Lett. 110, 130401 (2013).

  8. 8.

    , & Testing nonlocality of a single photon without a shared reference frame. Phys. Rev. A 88, 012111 (2013).

  9. 9.

    & Nonlocality of a single particle. Phys. Rev. Lett. 99, 180404 (2007).

  10. 10.

    & Nonlocal aspects of a quantum wave. Phys. Rev. A 61, 052108 (2000).

  11. 11.

    & Testing quantum nonlocality in phase space. Phys. Rev. Lett. 82, 2009–2013 (1999).

  12. 12.

    et al. Deterministic secure quantum communication with four-qubit W states. Int. J. Quant. Inf. 9, 607–614 (2011).

  13. 13.

    & Teleportation of an unknown state by W state. Phys. Lett. A 296, 161–164 (2002).

  14. 14.

    , , & Quantum teleportation via a W state. New J. Phys. 5, 136 (2005).

  15. 15.

    et al. Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57, 2368–2378 (1998).

  16. 16.

    & Possibility of coherent phenomena such as Bloch oscillations with single photons via W states. Phys. Rev. A 79, 053849 (2009).

  17. 17.

    , & Robust and scalable scheme to generate large-scale entanglement webs. Phys. Rev. A 83, 050303 (2011).

  18. 18.

    & Reading boundless error-free bits using a single photon. Phys. Rev. A 87, 062306 (2013).

  19. 19.

    et al. Characterization of multipartite entanglement for one photon shared among four optical modes. Science 324, 764–768 (2009).

  20. 20.

    , , , & Entanglement of spin waves among four quantum memories. Nature 468, 412–416 (2010).

  21. 21.

    , , & Quantum and classical correlations in waveguide lattices. Phys. Rev. Lett. 102, 253904 (2009).

  22. 22.

    , , , & Control of directional evanescent coupling in fs laser written waveguides. Opt. Express 15, 1579–1587 (2007).

  23. 23.

    et al. Fast physical random bit generation with chaotic semiconductor lasers. Nature Photon. 2, 728–732 (2008).

  24. 24.

    , , , & An optical ultrafast random bit generator. Nature Photon. 4, 58–61 (2010).

  25. 25.

    , , , & A fast and compact quantum random number generator. Rev. Sci. Instrum. 71, 1675–1680 (2000).

  26. 26.

    et al. Random numbers certified by Bell's theorem. Nature 464, 1021–1024 (2010).

  27. 27.

    , & Quantum random number generator using photon-number path entanglement. Appl. Opt. 48, 1774–1778 (2009).

  28. 28.

    et al. Einstein–Podolsky–Rosen spatial entanglement in ordered and Anderson photonic lattices. Phys. Rev. Lett. 110, 150503 (2013).

  29. 29.

    , , , & Generating photon-encoded W states in multiport waveguide-array systems. Phys. Rev. A 87, 013842 (2013).

  30. 30.

    , , , & Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

  31. 31.

    , , & Ultrafast processes for bulk modification of transparent materials. MRS Bull. 31, 620–625 (2006).

  32. 32.

    et al. Laser written waveguide photonic quantum circuits. Opt. Express 17, 12546–12554 (2009).

  33. 33.

    et al. Two-particle bosonic–fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012).

  34. 34.

    , , & Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubit. Sci. Rep. 4, 4118 (2014).

  35. 35.

    , , , & Demonstration of the complementarity of one- and two-photon interference. Phys. Rev. A 63, 063803 (2001).

  36. 36.

    et al. Observation of topologically protected bound states in photonic quantum walks. Nature Commun. 3, 882 (2012).

  37. 37.

    Coherence and indistinguishability. Opt. Lett. 16, 1882–1883 (1991).

  38. 38.

    et al. Verifying multipartite mode entanglement of W states. New J. Phys. 11, 063029 (2009).

  39. 39.

    Linear optical scheme to demonstrate genuine multipartite entanglement for single-particle W states. Phys. Rev. A 77, 062328 (2008).

  40. 40.

    & Entanglement detection. Phys. Rep. 474, 1–75 (2009).

  41. 41.

    et al. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (revised) (National Institute of Standards and Technology (U.S.) Special Publication 800-22rev1, 2010); available at .

  42. 42.

    & Chaotic lasers: the world's fastest dice. Nature Photon. 2, 714–715 (2008).

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Acknowledgements

The authors thank K. Schwaiger, B. Kraus and G. Weihs for helpful discussions. Financial support by the German Ministry of Education and Research (Center for Innovation Competence programme, grant no. 03Z1HN31), the Thuringian Ministry for Education, Science and Culture (Research group Spacetime, grant no. 11027-514), the Deutsche Forschungsgemeinschaft (grant no. NO462/6-1), the German–Israeli Foundation for Scientific Research and Development (grant no. 1157-127.14/2011) and the M. Heinrich was supported by the German National Academy of Sciences Leopoldina (grant no. LPDS 2012-01) is gratefully acknowledged.

Author information

Author notes

    • Markus Gräfe
    • , René Heilmann
    •  & Armando Perez-Leija

    These authors contributed equally to this work

Affiliations

  1. Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena 07743, Germany

    • Markus Gräfe
    • , René Heilmann
    • , Armando Perez-Leija
    • , Robert Keil
    • , Felix Dreisow
    • , Matthias Heinrich
    • , Stefan Nolte
    •  & Alexander Szameit
  2. Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria

    • Robert Keil
  3. CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, Florida 32816, USA

    • Matthias Heinrich
    •  & Demetrios N. Christodoulides
  4. INAOE, Coordinacion de Optica, Luis Enrique Erro No. 1, Tonantzintla, Puebla 72840, Mexico.

    • Hector Moya-Cessa

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Contributions

M.G., R.H., A.P.-L. and D.N.C. conceived the idea. M.G., R.H and R.K. designed the samples and performed the measurements. A.P.-L., M.G., R.H and R.K. analysed the data. A.S. supervised the project. All authors discussed the results and co-wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Alexander Szameit.

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DOI

https://doi.org/10.1038/nphoton.2014.204

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