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

Journal name:
Nature Photonics
Volume:
8,
Pages:
364–368
Year published:
DOI:
doi:10.1038/nphoton.2014.81
Received
Accepted
Published online
Corrected online

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.

At a glance

Figures

  1. Scheme for encoding the C-GHZ state [verbar][phiv]N,2+[rang] with physical qubits.
    Figure 1: Scheme for encoding the C-GHZ state |ϕN,2+right fence with physical qubits.

    a, Creation of logical state |0right fenceL with a ‘Hadamard-like’ gate on |+right fenceL. This ‘Hadamard-like’ gate can be realized with a Hadamard gate and a CNOT gate on the two physical qubits at initial state |+right fenceL = |00right fenceP. b, CNOT operation between |+right fenceL and |0right fenceL. This can be realized by four physical qubits with one Hadamard gate and three CNOT gates. This is also equivalent to the preparation of |ϕ2,2+right fence. c, Quantum circuit for encoding |ϕ3,2+right fence with six physical qubits. d, Quantum circuit for encoding |ϕN,2+right fence.

  2. Experimental set-up to prepare and characterize the three-logical-qubit C-GHZ state [verbar][phiv]3,2+[rang].
    Figure 2: Experimental set-up to prepare and characterize the three-logical-qubit C-GHZ state |ϕ3,2+right fence.

    a, An ultraviolet pulse (130 fs, 76 MHz, 390 nm) passes through three 2-mm-thick BBO crystals, creating three pairs of entangled photons. Photons 1′ and 4′ are superposed on the PBS to generate |GHZright fence4. The CNOT gates applied between 1′′–5′ and 4′′–6′ are realized by a combination of optical elements including two HWPs and three PDBSs. The different path lengths of the overlapping photons are finely adjusted, sequentially. b, Ultra-bright entanglement source. The initial entangled photon pair is generated by SPDC. Each photon is well compensated by setting an HWP and a 1-mm-thick BBO crystal in each path. One photon's polarization is rotated by 90° using an HWP. By superposing two photons on a PBS, a high-brightness entangled photon pair is obtained10. c, Polarization analyser for each output photon. Output photons are guided to a PBS passing through a QWP and an HWP, and then well coupled into two single-mode fibres and finally detected by two single-photon counting modules (not shown). d, Set-up for engineered collective noise. An HWP is sandwiched by two QWPs to create an arbitrary single-qubit unitary transformation. e, Symbols used in the figure.

  3. Experimental results for creating the three-logical-qubit C-GHZ state.
    Figure 3: Experimental results for creating the three-logical-qubit C-GHZ state.

    a, Measured sixfold coincidence in the H/V basis. b, Expectation values for different measurement settings (see Supplementary Section II). Error bars represent statistical errors (±1 s.d.).

  4. Evolution of the C-GHZ state under simulated noise in comparison with the normal GHZ state.
    Figure 4: Evolution of the C-GHZ state under simulated noise in comparison with the normal GHZ state.

    a, Theoretical calculated curves of the dynamics for fidelities F12, F13 and F23 evolving under simulated noise with ideal states |ϕ3,2+right fence and |GHZright fence3 (blue and red solid lines, respectively). b, Measured results for F12, F13 and F23 of generated C-GHZ state ρ1L2L3L at different noise levels in the experiment. The dash-dotted line is the dynamic curve calculated with an imperfect initial state at |ϕ3,2+right fence with a fidelity of 56%, which is evolved from an ideal state |ϕ3,2+right fence under white-noise (see Supplementary Section IV). c, Measured F12, F13 and F23 of generated |GHZright fence3 at different noise levels. The dash-dotted line is the dynamic curve calculated with an imperfect initial state at |GHZright fence3 with a fidelity of 91%, which is evolved from an ideal three-photon GHZ state under white-noise (see Supplementary Section IV). d, Intuitive perspective of the fidelities of |ϕ3,2+right fence and |GHZright fence3 obtained by averaging F12, F13 and F23.

Change history

Corrected online 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 (|0right fence⊗N + |1right fence⊗N)/√2.

Similarly, equation (1) should appear as |ϕ±N,mright fence = (|GHZ+mright fence⊗N ±|GHZmright fence⊗N)/√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 (|0right fence⊗m ± |1right fence⊗m)/√2.

In equation (2), the two symbols “3” should not be superscripted relative to the symbol "⊗". The correct expression is
|ϕ+3,2right fence = (|Φ+right fence⊗3 + |Φright fence⊗3)/√2 = (|HHHHHHright fence + |HHVVVVright fence +  |VVVVHHright fence + |VVHHVVright fence)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 = eiθσy.

These typographical errors have been corrected in both the HTML and PDF versions of this Letter.

References

  1. Greenberger, D. M., Horne, M. A. & Zeilinger, A. in Bell's Theorem, Quantum Theory, and Conceptions of the Universe 6972 (ed. Kafatos, M.) (Kluwer, 1989).
  2. Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777838 (2012).
  3. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 13301336 (2004).
  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).
  5. Zhao, Z. et al. Experimental demonstration of five-photon entanglement and open-destination teleportation. Nature 430, 5458 (2004).
  6. Dür, W., Simon, C. & Cirac, J. I. Effective size of certain macroscopic quantum superpositions. Phys. Rev. Lett. 89, 210402 (2002).
  7. Dür, W. & Briegel, H.-J. Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2004).
  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).
  9. Fröwis, F. & Dür, W. Stable macroscopic quantum superpositions. Phys. Rev. Lett. 106, 110402 (2011).
  10. Yao, X.-C. et al. Observation of eight-photon entanglement. Nature Photon. 6, 225228 (2012).
  11. Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
  12. Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 38653868 (1997).
  13. Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007).
  14. Zanardi, P. & Rasetti, M. Noiseless quantum codes. Phys. Rev. Lett. 79, 33063309 (1997).
  15. Lidar, D. A., Chuang, I. L. & Whaley, K. B. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 25942597 (1998).
  16. Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493R2496 (1995).
  17. Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198201 (1996).
  18. Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 38243851 (1996).
  19. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 43374341 (1995).
  20. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 51885191 (2001).
  21. Hofmann, H. F. & Takeuchi, S. Quantum phase gate for photonic qubits using only beam splitters and postselection. Phys. Rev. A 66, 024308 (2002).
  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).
  23. Kiesel, N., Schmid, C., Weber, U., Ursin, R. & Weinfurter, H. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005).
  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).
  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).
  26. Bourennane, M. et al. Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92, 087902 (2004).
  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).
  28. Dür, W., Cirac, J. I. & Tarrach, R. Separability and distillability of multiparticle quantum systems. Phys. Rev. Lett. 83, 35623565 (1999).

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Author information

  1. These authors contributed equally to this work

    • He Lu &
    • Luo-Kan Chen

Affiliations

  1. Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

    • He Lu,
    • Luo-Kan Chen,
    • Chang Liu,
    • Ping Xu,
    • Xing-Can Yao,
    • Li Li,
    • Nai-Le Liu,
    • Bo Zhao,
    • Yu-Ao Chen &
    • Jian-Wei Pan
  2. Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, 201315, China

    • He Lu,
    • Luo-Kan Chen,
    • Chang Liu,
    • Ping Xu,
    • Xing-Can Yao,
    • Li Li,
    • Nai-Le Liu,
    • Bo Zhao,
    • Yu-Ao Chen &
    • Jian-Wei Pan

Contributions

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.

Competing financial interests

The authors declare no competing financial interests.

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