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Scalable multiparticle entanglement of trapped ions

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.

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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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Correspondence to H. Häffner.

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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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