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Bell's inequality violation with spins in silicon

Abstract

Bell's theorem proves the existence of entangled quantum states with no classical counterpart1. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing2,3,4. We demonstrate a Bell/ Clauser–Horne–Shimony–Holt inequality5 violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.

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Figure 1: Device operation and state preparation protocols.
Figure 2: Bell's inequality violation.
Figure 3: Density matrix tomography.

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Acknowledgements

This research was funded by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project no. CE110001027) and the US Army Research Office (W911NF-13-1-0024). The authors acknowledge support from the Australian National Fabrication Facility. The work at Keio was supported in part by a Grant-in-Aid for Scientific Research by MEXT, in part by NanoQuine, in part by FIRST, and in part by a JSPS Core-to-Core Program.

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Contributions

J.P.D. and S.S. contributed equally to this work, designing and carrying out the experiments, and analysing the data, with A.M.'s supervision. J.P.D., J.T.M., A.L. and A.M. designed and constructed the experimental set-up. R.K. and F.H. fabricated the device with A.S.D.'s supervision. K.M.I. supplied the 28Si wafers. D.N.J. and J.C.M. designed and carried out the 31P ion implantation with R.K.’s help. J.P.D., S.S. and A.M. wrote the manuscript with feedback from all authors.

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Correspondence to Andrea Morello.

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The authors declare no competing financial interests.

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Dehollain, J., Simmons, S., Muhonen, J. et al. Bell's inequality violation with spins in silicon. Nature Nanotech 11, 242–246 (2016). https://doi.org/10.1038/nnano.2015.262

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