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On-chip generation of high-order single-photon W-states

Nature Photonics volume 8, pages 791–795 (2014)Cite this article

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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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Figure 1: Schematic of the experimental set-up.
Figure 2: Generation of high-order photonic W-states on an integrated platform.
Figure 3: Interferometric validation of W-states, given a priori knowledge of a single-photon input state.

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. Walter, M., Doran, B., Gross, D. & Christandl, M. Entanglement polytopes: multiparticle entanglement from single-particle information. Science 340, 1205–1208 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  2. Afek, I., Ambar, O. & Silberberg, Y. High-NOON states by mixing quantum and classical light. Science 328, 879–881 (2010).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Carteret, H. A., Linden, N., Popescu, S. & Sudbery, A. Multiparticle entanglement. Found. Phys. 29, 527–552 (1999).

    Article  MathSciNet  Google Scholar 

  5. Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Brask, J. B., Chaves, R. & Brunner, N. Testing nonlocality of a single photon without a shared reference frame. Phys. Rev. A 88, 012111 (2013).

    Article  ADS  Google Scholar 

  9. Dunningham, J. & Vedral, V. Nonlocality of a single particle. Phys. Rev. Lett. 99, 180404 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  10. Aharonov, Y. & Vaidman, L. Nonlocal aspects of a quantum wave. Phys. Rev. A 61, 052108 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  14. Joo, J., Park, Y., Oh, S. & Kim, J. Quantum teleportation via a W state. New J. Phys. 5, 136 (2005).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Fujii, K., Maeda, H. & Yamamoto, K. Robust and scalable scheme to generate large-scale entanglement webs. Phys. Rev. A 83, 050303 (2011).

    Article  ADS  Google Scholar 

  18. Guha, S. & Shapiro, J. H. Reading boundless error-free bits using a single photon. Phys. Rev. A 87, 062306 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Choi, K. S., Goban, A., Papp, S. B., van Enk, S. J. & Kimble, H. J. Entanglement of spin waves among four quantum memories. Nature 468, 412–416 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Szameit, A., Dreisow, F., Pertsch, T., Nolte, S. & Tünnermann, A. Control of directional evanescent coupling in fs laser written waveguides. Opt. Express 15, 1579–1587 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. Kanter, I., Aviad, Y., Reidler, I., Cohen, E. & Rosenbluh, M. An optical ultrafast random bit generator. Nature Photon. 4, 58–61 (2010).

    Article  ADS  Google Scholar 

  25. Jennewein, T., Achleitner, U., Weihs, G., Weinfurter, H. & Zeilinger, A. A fast and compact quantum random number generator. Rev. Sci. Instrum. 71, 1675–1680 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. Kwon, O., Cho, Y. W. & Kim, Y. H. Quantum random number generator using photon-number path entanglement. Appl. Opt. 48, 1774–1778 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. Perez-Leija, A., Hernandez-Herrejon, J. C., Moya-Cessa, H., Szameit, A. & Christodoulides, D. N. Generating photon-encoded W states in multiport waveguide-array systems. Phys. Rev. A 87, 013842 (2013).

    Article  ADS  Google Scholar 

  30. Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O'Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

    Article  ADS  Google Scholar 

  31. Itoh, K., Watanabe, W., Nolte, S. & Schaffer, C. B. Ultrafast processes for bulk modification of transparent materials. MRS Bull. 31, 620–625 (2006).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. Heilmann, R., Gräfe, M., Nolte, S. & Szameit, A. Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubit. Sci. Rep. 4, 4118 (2014).

    Article  ADS  Google Scholar 

  35. Abouraddy, A. F., Nasr, M. B., Saleh, B. E. A., Sergienko, A. V. & Teich, M. C. Demonstration of the complementarity of one- and two-photon interference. Phys. Rev. A 63, 063803 (2001).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  40. Gühne, O. & Tóth, G. Entanglement detection. Phys. Rep. 474, 1–75 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  41. Rukhin, A. 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 http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html.

    Google Scholar 

  42. Murphy, T. E. & Roy, R. Chaotic lasers: the world's fastest dice. Nature Photon. 2, 714–715 (2008).

    Article  ADS  Google Scholar 

Download references

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

  1. Markus Gräfe, René Heilmann and Armando Perez-Leija: These authors contributed equally to this work

Authors and 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, 32816, Florida, USA

    Matthias Heinrich & Demetrios N. Christodoulides

  4. INAOE, Coordinacion de Optica, Luis Enrique Erro No. 1, Tonantzintla, 72840, Puebla, Mexico

    Hector Moya-Cessa

Authors
  1. Markus Gräfe
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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.

Corresponding author

Correspondence to Alexander Szameit.

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The authors declare no competing financial interests.

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Gräfe, M., Heilmann, R., Perez-Leija, A. et al. On-chip generation of high-order single-photon W-states. Nature Photon 8, 791–795 (2014). https://doi.org/10.1038/nphoton.2014.204

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