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.

Experimental non-classicality of an indivisible quantum system

Nature volume 474, pages 490–493 (2011)Cite this article

Subjects

Abstract

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact1. Alternatives have been explored—notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results2,3,4,5 imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found6,7,8,9,10 and tested experimentally11,12 with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced13 and tested experimentally14,15,16. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits17,18 which provides evidence that no joint probability distribution describing the outcomes of all possible measurements—and, therefore, no non-contextual theory—can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky19. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

Rent or Buy

All prices are NET prices.

Figure 1: Experimental preparation and five successive measurement stages.
Figure 2: Representation of the measurements and a state providing maximal violation of the inequality (2) by directions in three-dimensional space19.
Figure 3: Experimental set-up.

References

  1. 1

    Heisenberg, W. The Physical Principles of Quantum Theory 13–52 (Univ. Chicago Press, 1930)

    MATH  Google Scholar 

  2. 2

    Specker, E. Die Logik nicht gleichzeitig entscheidbarer Aussagen. Dialectica 14, 239–246 (1960)

    MathSciNet  Article  Google Scholar 

  3. 3

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

  4. 4

    Kochen, S. & Specker, E. P. The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MathSciNet  MATH  Google Scholar 

  5. 5

    Gleason, A. M. Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885–893 (1957)

    MathSciNet  MATH  Google Scholar 

  6. 6

    Mermin, N. D. Simple unified form for the major no-hidden-variables theorems. Phys. Rev. Lett. 65, 3373–3376 (1990)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  7. 7

    Peres, A. Two simple proofs of the Kochen-Specker theorem. J. Phys. A 24, L175–L178 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  8. 8

    Peres, A. Quantum Theory: Concepts and Methods Ch. 7 (Kluwer, 1993)

    MATH  Google Scholar 

  9. 9

    Clifton, R. Getting contextual and nonlocal elements-of-reality the easy way. Am. J. Phys. 61, 443–447 (1993)

    ADS  Article  Google Scholar 

  10. 10

    Cabello, A., Estebaranz, J. M. & García-Alcaine, G. Bell-Kochen-Specker theorem: a proof with 18 vectors. Phys. Lett. A 212, 183–187 (1996)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. 11

    Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W. & Guo, G.-C. Experimental test of the Kochen-Specker theorem with single photons. Phys. Rev. Lett. 90, 250401 (2003)

    ADS  Article  Google Scholar 

  12. 12

    Bartosik, H. et al. Experimental test of quantum contextuality in neutron interferometry. Phys. Rev. Lett. 103, 040403 (2009)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Cabello, A. Experimentally testable state-independent quantum contextuality. Phys. Rev. Lett. 101, 210401 (2008)

    ADS  Article  Google Scholar 

  14. 14

    Kirchmair, G. et al. State-independent experimental test of quantum contextuality. Nature 460, 494–497 (2009)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Amselem, E., Rådmark, M., Bourennane, M. & Cabello, A. State-independent quantum contextuality with single photons. Phys. Rev. Lett. 103, 160405 (2009)

    ADS  Article  Google Scholar 

  16. 16

    Moussa, O., Ryan, C. A., Cory, D. G. & Laflamme, R. Testing contextuality on quantum ensembles with one clean qubit. Phys. Rev. Lett. 104, 160501 (2010)

    ADS  MathSciNet  Article  Google Scholar 

  17. 17

    Lapkiewicz, R. et al. Most Basic Experimental Falsification of Non-Contextuality (Poster, 13th Workshop on Quantum Information Processing, 2010)

  18. 18

    Lapkiewicz, R. et al. Experimental Non-Classicality of an Indivisible System. Abstr. Q29.00008 (41st Annu. Meeting Div. Atom. Mol. Opt. Phys., American Physical Society, 2010)

  19. 19

    Klyachko, A. A., Can, M. A., Biniciog˘lu, S. & Shumovsky, A. S. Simple test for hidden variables in spin-1 systems. Phys. Rev. Lett. 101, 20403 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  20. 20

    Gühne, O. et al. Compatibility and noncontextuality for sequential measurements. Phys. Rev. A 81, 22121 (2010)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the ERC (Advanced Grant QIT4QAD), the Austrian Science Fund (Grant F4007), the EC (Marie Curie Research Training Network EMALI), the Vienna Doctoral Program on Complex Quantum Systems and the John Templeton Foundation. We acknowledge A. A. Klyachko for discussion of the proposal made in ref. 19; M. Hentschel, M. Kacprowicz and G. J. Pryde for discussions of technical issues; A. Cabello, S. Osnaghi, H. M. Wiseman and M. Z˙ukowski, with whom we discussed the conceptual issues; and M. Nespoli for help during the early stages of the experiment.

Author information

Author notes

  1. Nathan K. Langford & Marcin Wieśniak

    Present address: Present addresses: Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK (N.K.L.); Institute of Theoretical Physics and Astrophysics, University of Gdansk, PL-80-952 Gdansk, Poland (M.W.).,

Affiliations

  1. Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria

    Radek Lapkiewicz, Peizhe Li, Christoph Schaeff, Nathan K. Langford, Sven Ramelow, Marcin Wieśniak & Anton Zeilinger

  2. Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090, Vienna, Austria

    Radek Lapkiewicz, Christoph Schaeff, Nathan K. Langford, Sven Ramelow & Anton Zeilinger

Authors
  1. Radek Lapkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peizhe Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christoph Schaeff
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nathan K. Langford
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sven Ramelow
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Marcin Wieśniak
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Anton Zeilinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the design of the experiment. R.L., P.L. and C.S. performed the experiment and all authors wrote the manuscript.

Corresponding author

Correspondence to Anton Zeilinger.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Text and Data 1-5, Supplementary Figure 1 with a legend and Supplementary Table 1. (PDF 522 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lapkiewicz, R., Li, P., Schaeff, C. et al. Experimental non-classicality of an indivisible quantum system. Nature 474, 490–493 (2011). https://doi.org/10.1038/nature10119

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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