Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Generation of hybrid entanglement of light

Nature Photonics volume 8, pages 564–569 (2014)Cite this article

Subjects

Abstract

Entanglement between quantum and classical objects is of special interest in the context of fundamental studies of quantum mechanics and potential applications for quantum information processing. In quantum optics, single photons are treated as light quanta while coherent states are considered the most classical of pure states. Recently, entanglement between a single photon and a coherent state in a free-travelling field was identified as a useful resource for optical quantum information processing. However, the extreme difficulty involved in generating such states was highlighted, as it requires clean cross-Kerr nonlinearities. Here, we devise and experimentally demonstrate a scheme to generate such hybrid entanglement by implementing a superposition of two distinct quantum operations. The generated states clearly show entanglement between the two different types of states. Our work opens the way to the generation of hybrid entanglement of greater size and the development of efficient quantum information processing using a new type of qubit.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Scheme for generating hybrid entanglement of light.
Figure 2: Experimental generation of hybrid entanglement of light using temporal modes.
Figure 3: Experimental hybrid entanglement.
Figure 4: Experimental symmetric hybrid entanglement.

Similar content being viewed by others

References

  1. Schrödinger, E. Die gegenwaertige Situation in der Quantenmechanik. Naturwissenschaften 23, 823–828 (1935).

    Article  ADS  Google Scholar 

  2. Glauber, R. J. Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  3. Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715–775 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  4. Lee, S.-W. & Jeong, H. Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits. Phys. Rev. A 87, 022326 (2013).

    Article  ADS  Google Scholar 

  5. Kwon, H. & Jeong, H. Violation of the Bell–Clauser–Horne–Shimony–Holt inequality using imperfect photodetectors with optical hybrid states. Phys. Rev. A 88, 052127 (2013).

    Article  ADS  Google Scholar 

  6. Bell, J. S. On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  7. Pearle, P. M. Hidden-variable example based upon data rejection. Phys. Rev. D 2, 1418–1425 (1970).

    Article  ADS  Google Scholar 

  8. Gerry, C. Generation of optical macroscopic quantum superposition states via state reduction with a Mach–Zehnder interferometer containing a Kerr medium. Phys. Rev. A 59, 4095–4098 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  9. Nemoto, K. & Munro, W. J. Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004).

    Article  ADS  Google Scholar 

  10. Jeong, H. Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation. Phys. Rev. A 72, 034305 (2005).

    Article  ADS  Google Scholar 

  11. Shapiro, J. H. Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73, 062305 (2006).

    Article  ADS  Google Scholar 

  12. Shapiro, J. H. & Razavi, M. Continuous-time cross-phase modulation and quantum computation. New J. Phys. 9, 16 (2007).

    Article  ADS  Google Scholar 

  13. Gea-Banacloche, J. Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A 81, 043823 (2010).

    Article  ADS  Google Scholar 

  14. Kreis, K. & van Loock, P. Classifying, quantifying, and witnessing qudit–qumode hybrid entanglement. Phys. Rev. A 85, 032307 (2012).

    Article  ADS  Google Scholar 

  15. Lee, C.-W. & Jeong, H. Quantification of macroscopic quantum superpositions within phase space. Phys. Rev. Lett. 106, 220401 (2011).

    Article  ADS  Google Scholar 

  16. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007).

    Article  ADS  Google Scholar 

  17. 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 

  18. Sekatski, P. et al. Exploring macroscopic entanglement with a single photon and coherent states. Phys. Rev. A 86, 060301 (2012).

    Article  ADS  Google Scholar 

  19. Bruno, N. et al. Displacing entanglement back and forth between the micro and macro domains. Nature Phys. 9, 545–548 (2013).

    Article  ADS  Google Scholar 

  20. Lvovsky, A. I., Ghobadi, R., Chandra, A., Prasad, A. S. & Simon, C. Observation of micro–macro entanglement of light. Nature Phys. 9, 541–544 (2013).

    Article  ADS  Google Scholar 

  21. Marquardt, F., Abel, B. & von Delft, J. Measuring the size of a quantum superposition of two many-body states. Phys. Rev. A 78, 012109 (2008).

    Article  ADS  Google Scholar 

  22. Nimmrichter, S. & Hornberger, K. Macroscopicity of mechanical quantum superposition states. Phys. Rev. Lett. 110, 160403 (2013).

    Article  ADS  Google Scholar 

  23. Sekatski, P., Sangouard, N. & Gisin, N. The size of quantum superpositions as measured with ‘classical’ detectors. Phys. Rev. A 89, 012116 (2014).

    Article  ADS  Google Scholar 

  24. Zavatta, A., Viciani, S. & Bellini, M. Quantum-to-classical transition with single-photon-added coherent states of light. Science 306, 660–662 (2004).

    Article  ADS  Google Scholar 

  25. Lamas-Linares, A., Simon, C., Howell, J. C. & Bouwmeester, D. Experimental quantum cloning of single photons. Science 296, 712–714 (2002).

    Article  ADS  Google Scholar 

  26. Parigi, V., Zavatta, A., Kim, M. S. & Bellini, M. Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890–1893 (2007).

    Article  ADS  Google Scholar 

  27. Zavatta, A., Parigi, V., Kim, M. S., Jeong, H. & Bellini, M. Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields. Phys. Rev. Lett. 103, 140406 (2009).

    Article  ADS  Google Scholar 

  28. Peres, A. Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  29. Horodecki, M., Horodecki, P. & Horodecki, R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  30. Lee, J., Kim, M. S., Park, Y. J. & Lee, S. Partial teleportation of entanglement in a noisy environment. J. Mod. Opt. 47, 2151–2164 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  31. Andersen, U. L. & Neergaard-Nielsen, J. S. Heralded generation of a micro–macro entangled state. Phys. Rev. A 88, 022337 (2013).

    Article  ADS  Google Scholar 

  32. Zavatta, A., D'Angelo, M., Parigi, V. & Bellini, M. Remote preparation of arbitrary time-encoded single-photon ebits. Phys. Rev. Lett. 96, 020502 (2006).

    Article  ADS  Google Scholar 

  33. Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B 6, S556–S559 (2004).

    Article  ADS  Google Scholar 

  34. Hradil, Z., Řeháček, J., Knill, E. & Lvovsky, A. I. Diluted maximum-likelihood algorithm for quantum tomography. Phys. Rev. A 75, 042108 (2007).

    Article  ADS  Google Scholar 

  35. Ralph, T. C., Gilchrist, A., Milburn, G. J., Munro, W. J. & Glancy, S. Quantum computation with coherent optical states. Phys. Rev. A 68, 042319 (2003).

    Article  ADS  Google Scholar 

  36. Neergaard-Nielsen, J. S., Eto, Y., Lee, C.-W., Jeong, H. & Sasaki, M. Quantum tele-amplification with a continuous-variable superposition state. Nature Photon. 7, 439–443 (2013).

    Article  ADS  Google Scholar 

  37. Takahashi, H. et al. Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction. Phys. Rev. Lett. 101, 233605 (2008).

    Article  ADS  Google Scholar 

  38. Gerrits, T. et al. Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum. Phys. Rev. A 82, 031802(R) 10.1103/PhysRevA.82.031802(2010).

    Article  ADS  Google Scholar 

  39. Park, K., Lee, S.-W. & Jeong, H. Quantum teleportation between particlelike and fieldlike qubits using hybrid entanglement under decoherence effects. Phys. Rev. A 86, 062301 (2012).

    Article  ADS  Google Scholar 

  40. Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    Article  ADS  Google Scholar 

  41. Ralph, T. C. & Pryde, G. J. Optical quantum computation. Prog. Opt. 54, 209–269 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

A.Z., L.S.C., S.G. and M.B. acknowledge support from the European Union under the CHIST-ERA (European Coordinated Research on Long-term Challenges in Information and Communication Sciences & Technologies ERA-Net) project QSCALE (Quantum Technologies for Extending the Range of Quantum Communications) and from the Italian Ministry of Education, University and Research under the FIRB (Fondo per gli Investimenti della Ricerca di Base; contract no. RBFR10M3SB). H.J., M.K. and S.-W.L. were supported by the National Research Foundation of Korea (grant no. 2010-0018295) funded by the Ministry of Science, ICT and Future Planning of Korea. T.C.R. acknowledges support from the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project no. CE110001027).

Author information

Author notes

  1. Samuele Grandi

    Present address: Present address: Centre for Cold Matter, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK,

Authors and Affiliations

  1. Department of Physics and Astronomy, Center for Macroscopic Quantum Control, Seoul National University, Seoul, 151-742, Korea

    Hyunseok Jeong, Minsu Kang & Seung-Woo Lee

  2. Istituto Nazionale di Ottica (INO-CNR), Largo Enrico Fermi 6, Florence, 50125, Italy

    Alessandro Zavatta, Luca S. Costanzo, Samuele Grandi & Marco Bellini

  3. LENS and Department of Physics, University of Firenze, Sesto Fiorentino, Florence, 50019, Italy

    Alessandro Zavatta, Luca S. Costanzo & Marco Bellini

  4. Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, Queensland, 4072, Australia

    Timothy C. Ralph

Authors
  1. Hyunseok Jeong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandro Zavatta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Minsu Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Seung-Woo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luca S. Costanzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Samuele Grandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Timothy C. Ralph
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Marco Bellini
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

H.J. and T.C.R. proposed the experiment and developed the theoretical models. M.K. and S.-W.L. performed theoretical analysis and numerical simulations. L.S.C. and S.G. ran the experiment and data analysis. A.Z. and M.B. proposed, planned and coordinated the experiment and data analysis. All authors discussed the results and implications of the experiment and contributed to writing the manuscript.

Corresponding authors

Correspondence to Hyunseok Jeong or Marco Bellini.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 628 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jeong, H., Zavatta, A., Kang, M. et al. Generation of hybrid entanglement of light. Nature Photon 8, 564–569 (2014). https://doi.org/10.1038/nphoton.2014.136

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2014.136

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing