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

## 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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## 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.

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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).

## Author information

Authors

### 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.

### Corresponding authors

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

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 512 kb)

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Reprints and Permissions

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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