Experimental realization of a concatenated Greenberger–Horne–Zeilinger state for macroscopic quantum superpositions

An Erratum to this article was published on 28 May 2014

This article has been updated

Abstract

The Greenberger–Horne–Zeilinger (GHZ) states1 play a significant role in fundamental tests of quantum mechanics2 and are one of the central resources of quantum-enhanced high-precision metrology3, fault-tolerant quantum computing4 and distributed quantum networks5. However, in a noisy environment, entanglement becomes fragile as the particle number increases6,7,8. Recently, a concatenated GHZ (C-GHZ) state, which retains the advantages of conventional GHZ states but is more robust in a noisy environment, was proposed9. Here, we experimentally prepare a three-logical-qubit C-GHZ state. By characterizing the dynamics of entanglement quality of the C-GHZ state under simple collective noise, we demonstrate that the C-GHZ state is more robust than the conventional GHZ state. Our work provides an essential tool for quantum-enhanced measurement and enables a new route to prepare and manipulate macroscopic entanglement. Our result is also useful for linear-optical quantum computation schemes whose building blocks are GHZ-type states.

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Figure 1: Scheme for encoding the C-GHZ state |ϕN,2+〉 with physical qubits.
Figure 2: Experimental set-up to prepare and characterize the three-logical-qubit C-GHZ state |ϕ3,2+〉.
Figure 3: Experimental results for creating the three-logical-qubit C-GHZ state.
Figure 4: Evolution of the C-GHZ state under simulated noise in comparison with the normal GHZ state.

Change history

  • 20 April 2014

    In the version of this Letter originally published in print, the following mathematical expressions were formatted incorrectly. On page 1, column 1, paragraph 2, line 2, the two symbols "N" should not be superscripted relative to the symbol "". The correct expression is (|0〉N + |1〉N)/√2. Similarly, equation (1) should appear as |ϕ±N,m〉 = (|GHZ+mN ±|GHZmN)/√2. On page 1, column 2, paragraph 1, line 3, the two symbols “m” should not be superscripted relative to the symbol "". The correct expression is (|0〉m ± |1〉m)/√2. In equation (2), the two symbols “3” should not be superscripted relative to the symbol "". The correct expression is |ϕ+3,2〉 = (|Φ+3 + |Φ3)/√2 = (|HHHHHH〉 + |HHVVVV〉 + |VVVVHH〉 + |VVHHVV〉)231456/2. In the expression for Uθ appearing on page 4, column 1, paragraph 3, line 5, the symbol "y" should be subscripted relative to the symbol "σ". The correct expression is Uθ = e i θ σ y . These typographical errors have been corrected in both the HTML and PDF versions of this Letter.

References

  1. 1

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

    Google Scholar 

  2. 2

    Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).

    ADS  Article  Google Scholar 

  3. 3

    Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004).

    ADS  Article  Google Scholar 

  4. 4

    Varnava, M., Browne, D. E. & Rudolph, T. How good must single photon sources and detectors be for efficient linear optical quantum computation? Phys. Rev. Lett. 100, 060502 (2008).

    ADS  Article  Google Scholar 

  5. 5

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

    ADS  Article  Google Scholar 

  6. 6

    Dür, W., Simon, C. & Cirac, J. I. Effective size of certain macroscopic quantum superpositions. Phys. Rev. Lett. 89, 210402 (2002).

    ADS  Article  Google Scholar 

  7. 7

    Dür, W. & Briegel, H.-J. Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2004).

    ADS  Article  Google Scholar 

  8. 8

    Aolita, L., Chaves, R., Cavalcanti, D., Acín, A. & Davidovich, L. Scaling laws for the decay of multiqubit entanglement. Phys. Rev. Lett. 100, 080501 (2008).

    ADS  Article  Google Scholar 

  9. 9

    Fröwis, F. & Dür, W. Stable macroscopic quantum superpositions. Phys. Rev. Lett. 106, 110402 (2011).

    ADS  Article  Google Scholar 

  10. 10

    Yao, X.-C. et al. Observation of eight-photon entanglement. Nature Photon. 6, 225–228 (2012).

    ADS  Article  Google Scholar 

  11. 11

    Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).

    ADS  Article  Google Scholar 

  12. 12

    Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865–3868 (1997).

    ADS  Article  Google Scholar 

  13. 13

    Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007).

    ADS  Article  Google Scholar 

  14. 14

    Zanardi, P. & Rasetti, M. Noiseless quantum codes. Phys. Rev. Lett. 79, 3306–3309 (1997).

    ADS  Article  Google Scholar 

  15. 15

    Lidar, D. A., Chuang, I. L. & Whaley, K. B. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998).

    ADS  Article  Google Scholar 

  16. 16

    Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).

    ADS  Article  Google Scholar 

  17. 17

    Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198–201 (1996).

    ADS  Article  Google Scholar 

  18. 18

    Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  19. 19

    Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Article  Google Scholar 

  20. 20

    Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

    ADS  Article  Google Scholar 

  21. 21

    Hofmann, H. F. & Takeuchi, S. Quantum phase gate for photonic qubits using only beam splitters and postselection. Phys. Rev. A 66, 024308 (2002).

    ADS  Article  Google Scholar 

  22. 22

    Langford, N. K. et al. Demonstration of a simple entangling optical gate and its use in Bell-state analysis. Phys. Rev. Lett. 95, 210504 (2005).

    ADS  Article  Google Scholar 

  23. 23

    Kiesel, N., Schmid, C., Weber, U., Ursin, R. & Weinfurter, H. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005).

    ADS  Article  Google Scholar 

  24. 24

    Okamoto, R., Hofmann, H. F., Takeuchi, S. & Sasaki, K. Demonstration of an optical quantum controlled-NOT gate without path interference. Phys. Rev. Lett. 95, 210506 (2005).

    ADS  Article  Google Scholar 

  25. 25

    Hofmann, H. F. Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations. Phys. Rev. Lett. 94, 160504 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26

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

    ADS  Article  Google Scholar 

  27. 27

    Gühne, O., Lu, C.-Y., Gao, W.-B. & Pan, J.-W. Toolbox for entanglement detection and fidelity estimation. Phys. Rev. A 76, 030305 (2007).

    ADS  Article  Google Scholar 

  28. 28

    Dür, W., Cirac, J. I. & Tarrach, R. Separability and distillability of multiparticle quantum systems. Phys. Rev. Lett. 83, 3562–3565 (1999).

    ADS  Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China, the CAS, the National Fundamental Research Program (grant no. 2011CB921300).

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H.L., L.-K.C., N.-L.L., Y.-A.C. and J.-W.P. conceived and designed the experiments. H.L., L.-K.C., C.L., P.X., X.-C.Y. and L.L. carried out the experiments. All authors analysed the data and wrote the paper. N.-L.L., Y.-A.C. and J.-W.P. supervised the whole project.

Corresponding authors

Correspondence to Nai-Le Liu or Yu-Ao Chen or Jian-Wei Pan.

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The authors declare no competing financial interests.

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Lu, H., Chen, L., Liu, C. et al. Experimental realization of a concatenated Greenberger–Horne–Zeilinger state for macroscopic quantum superpositions. Nature Photon 8, 364–368 (2014). https://doi.org/10.1038/nphoton.2014.81

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