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Hybrid quantum logic and a test of Bell’s inequality using two different atomic isotopes


Entanglement is one of the most fundamental properties of quantum mechanics1,2,3, and is the key resource for quantum information processing4,5 (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced6,7,8,9,10,11,12. Here we use a deterministic quantum logic gate to generate a ‘hybrid’ entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell’s inequality with non-identical atoms. We use a laser-driven two-qubit gate13, whose mechanism is insensitive to the qubits’ energy splittings, to produce a maximally entangled state of one 40Ca+ qubit and one 43Ca+ qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser–Horne–Shimony–Holt)14 version of Bell’s inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole8 but not the locality loophole7. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units15,16. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing.

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Figure 1: Calcium ion energy levels and experimental geometry.
Figure 2: Entangling gate sequence and results.
Figure 3: Density matrix of the mixed-isotope Bell state.

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This work was supported by the UK EPSRC ‘Networked Quantum Information Technology’ Hub and the US Army Research Office (contract W911NF-14-1-0217). D.M.L. thanks A. Castillo and E. A. Castillo for their hospitality while revising the manuscript.

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All authors contributed to the development of the apparatus and/or the design of the experiments. J.P.H. and D.M.L. conceived the experiments and took preliminary data. C.J.B. and V.M.S. designed and performed the experiments described here, analysed data and produced the figures. C.J.B. and D.M.L. wrote the manuscript, which all authors discussed.

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Correspondence to C. J. Ballance.

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Ballance, C., Schäfer, V., Home, J. et al. Hybrid quantum logic and a test of Bell’s inequality using two different atomic isotopes. Nature 528, 384–386 (2015).

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