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Scalable multiparticle entanglement of trapped ions

Nature volume 438, pages 643–646 (2005)Cite this article

Abstract

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven1,2,3. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions4 or five photons5 has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the ‘W state’6,7,8 plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing9 and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography10, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, ‘Greenberger–Horne–Zeilinger’ entangled states11 with up to six ions have been created and analysed in Boulder12.

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Figure 1: Absolute values, | ρ |, of the reconstructed density matrix of a | W 8 〉 state as obtained from quantum state tomography.

References

  1. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812 (1935)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 844–849 (1935)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  5. Zhao, Z. et al. Experimental demonstration of five-photon entanglement and open-destination teleportation. Nature 430, 54–58 (2004)

    Article  ADS  CAS  Google Scholar 

  6. 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 

  7. Zeilinger, A., Horne, M. A. & Greenberger, D. M. Higher-order quantum entanglement. NASA Conf. Publ. 3135, 73–81 (1992)

    Google Scholar 

  8. Roos, C. F. et al. Control and measurement of three–qubit entangled states. Science 304, 1478–1480 (2004)

    Article  ADS  CAS  Google Scholar 

  9. Bennett, C. H. & DiVincenzo, D. P. Quantum information and computation. Nature 404, 247–255 (2000)

    Article  ADS  CAS  Google Scholar 

  10. Roos, C. F. et al. Bell states of atoms with ultralong lifetimes and their tomographic state analysis. Phys. Rev. Lett. 92, 220402 (2004)

    Article  ADS  CAS  Google Scholar 

  11. Greenberger, D. M., Horne, M. & Zeilinger, A. in Bell's Theorem, Quantum Theory, and Conceptions of the Universe (ed. Kafatos, M.) 69–72 (Kluwer Academic, Dordrecht, 1989)

    Google Scholar 

  12. Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature doi:10.1038/nature 04251 (this issue)

  13. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 000910 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Sen(De), A. et al. Multiqubit W states lead to stronger nonclassicality than Greenberger–Horne–Zeilinger states. Phys. Rev. A 68, 062306 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  15. Joo, J., Park, Y.-J., Lee, J., Jang, J. & Kim, I. Quantum secure communication via a W state. J. Korean Phys. Soc. 46, 763–768 (2005)

    Google Scholar 

  16. Joo, J., Lee, J., Jang, J. & Park, Y.-J. Quantum secure communication with W States. Preprint at http://arxiv.org/quant-ph/0204003 (2002).

  17. Buhrman, H., van Dam, W., Høyer, P. & Tapp, A. Multiparty quantum communication complexity. Phys. Rev. A 60, 2737–2741 (1999)

    Article  ADS  CAS  Google Scholar 

  18. Schmidt-Kaler, F. et al. How to realize a universal quantum gate with trapped ions. Appl. Phys. B 77, 789–796 (2003)

    Article  ADS  CAS  Google Scholar 

  19. Fano, U. Description of states in quantum mechanics by density matrix and operator techniques. Rev. Mod. Phys. 29, 74–93 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  20. Hradil, Z., Reháček, J., Fiurášek, J. & Ježek, M. Maximum-likelihood methods in quantum mechanics. Lect. Notes Phys. 649, 59–112 (2004)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  22. Terhal, B. M. Bell inequalities and the separability criterion. Phys. Lett. A 271, 319–326 (2000)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Bourennane, M. et al. Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92, 087902 (2004)

    Article  ADS  Google Scholar 

  24. Dür, W. & Cirac, J. I. Classification of multiqubit mixed states: Separability and distillability properties. Phys. Rev. A 61, 042314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  25. Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    Article  ADS  CAS  Google Scholar 

  26. Miyake, A. & Briegel, H.-J. Distillation of multipartite entanglement by complementary stabilizer measurements. Preprint at http://arxiv.org/quant-ph/0506092 (2005).

  27. Dür, W. & Cirac, J. I. Multiparticle entanglement and its experimental detection. J. Phys. A 34, 6837–6850 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  28. Koashi, M., Bužek, V. & Imoto, N. Entangled webs: Tight bound for symmetric sharing of entanglement. Phys. Rev. A 62, 050302 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  29. Gulde, S. et al. Implementing the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge support by the Austrian Science Fund (FWF), by the European Commission (QGATES, CONQUEST, PROSECCO, QUPRODIS and OLAQUI networks), by the Institut für Quanteninformation GmbH, the DFG, and the ÖAW through project APART (W.D.). This material is based on work supported in part by the US Army Research Office. We thank P. Pham for the pulse modulation programmer, and A. Ostermann, M. Thalhammer and M. Ježek for help with the iterative reconstruction.

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Author notes

  1. C. Becher

    Present address: Fachrichtung Technische Physik, Universität des Saarlandes, Postfach 151150, D-66041, Saarbrücken, Germany

Authors and Affiliations

  1. Institut für Experimentalphysik,

    H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher & R. Blatt

  2. Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A–6020, Innsbruck, Austria

    W. Dür

  3. Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Technikerstraße 21a, A–6020, Innsbruck, Austria

    H. Häffner, C. F. Roos, J. Benhelm, T. Körber, U. D. Rapol, O. Gühne, W. Dür & R. Blatt

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Supplementary information

Supplementary Data 1

This file contains the real parts of the 4-ion density matrices. W4rho corresponds to the real part of DD...D|rho|DD...D. (TXT 4 kb)

Supplementary Data 2

This file contains the imaginary parts of the 4-ion density matrices. W4rho corresponds to the imaginary part of DD...D|rho|DD...D. (TXT 4 kb)

Supplementary Data 3

This file contains the real parts of the 5-ion density matrices. W5rho corresponds to the real part of DD...D|rho|DD...D. (TXT 9 kb)

Supplementary Data 4

This file contains the imaginary parts of the 5-ion density matrices. W5rho corresponds to the imaginary part of DD...D|rho|DD...D. (TXT 9 kb)

Supplementary Data 5

This file contains the real parts of the 6-ion density matrices. W6rho corresponds to the real part of DD...D|rho|DD...D. (TXT 37 kb)

Supplementary Data 6

This file contains the imaginary parts of the 6-ion density matrices. W6rho corresponds to the imaginary part of DD...D|rho|DD...D. (TXT 38 kb)

Supplementary Data 7

This file contains the real parts of the 7-ion density matrices. W7rho corresponds to the real part of DD...D|rho|DD...D. (TXT 256 kb)

Supplementary Data 8

This file contains the imaginary parts of the 7-ion density matrices. W7rho corresponds to the imaginary part of DD...D|rho|DD...D. (TXT 256 kb)

Supplementary Data 9

This file contains the real parts of the 8-ion density matrices. W8rho corresponds to the real part of DD...D|rho|DD...D. (TXT 1024 kb)

Supplementary Data 10

This file contains the imaginary parts of the 8-ion density matrices. W8rho corresponds to the imaginary part of DD...D|rho|DD...D. (TXT 1024 kb)

Supplementary Data 11

The files contain the real part of the entanglement witness used for detecting 8-ion entanglement. (TXT 1600 kb)

Supplementary Data 12

The files contain the imaginary part of the entanglement witness used for detecting 8-ion entanglement. (TXT 1600 kb)

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Häffner, H., Hänsel, W., Roos, C. et al. Scalable multiparticle entanglement of trapped ions. Nature 438, 643–646 (2005). https://doi.org/10.1038/nature04279

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