Abstract
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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References
Schrödinger, E. Discussion of probability relations between separated systems. Math. Proc. Camb. Phil. Soc. 31, 555–563 (1935)
Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)
Deutsch, D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)
Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Freedman, S. J. & Clauser, J. F. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972)
Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982)
Rowe, M. A. et al. Experimental violation of a Bell’s inequality with efficient detection. Nature 409, 791–794 (2001)
Moehring, D. L., Madsen, M., Blinov, B. & Monroe, C. Experimental Bell inequality violation with an atom and a photon. Phys. Rev. Lett. 93, 090410 (2004)
Giustina, M. et al. Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227–230 (2013)
Christensen, B. G. et al. Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett. 111, 130406 (2013)
Pfaff, W. et al. Demonstration of entanglement-by-measurement of solid-state qubits. Nature Phys. 9, 29–33 (2013)
Leibfried, D. et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003)
Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)
Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103, 259–328 (1998)
Monroe, C. & Kim, J. Scaling the ion trap quantum processor. Science 339, 1164–1169 (2013)
Matsukevich, D. N., Maunz, P., Moehring, D. L., Olmschenk, S. & Monroe, C. Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett. 100, 150404 (2008)
Lanyon, B. P. et al. Experimental violation of multipartite Bell inequalities with trapped ions. Phys. Rev. Lett. 112, 100403 (2014)
Blatt, R. & Wineland, D. J. Entangled states of trapped atomic ions. Nature 453, 1008–1015 (2008)
Harty, T. P. et al. High-fidelity preparation, gates, memory, and readout of a trapped-ion quantum bit. Phys. Rev. Lett. 113, 220501 (2014)
Ballance, C. J., Harty, T. P., Linke, N. M. & Lucas, D. M. High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions. Preprint at http://arXiv.org/abs/1406.5473 (2014)
Barrett, M. D. et al. Sympathetic cooling of 9Be+ and 24Mg+ for quantum logic. Phys. Rev. A 68, 042302 (2003)
Home, J. P. et al. Complete methods set for scalable ion trap quantum information processing. Science 325, 1227–1230 (2009)
Langer, C. et al. Long-lived qubit memory using atomic ions. Phys. Rev. Lett. 95, 060502 (2005)
Schmidt, P. O. et al. Spectroscopy using quantum logic. Science 309, 749–752 (2005)
Hume, D. B., Rosenband, T. & Wineland, D. J. High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements. Phys. Rev. Lett. 99, 120502 (2007)
Ballance, C. J. High-Fidelity Quantum Logic in Ca+. D.Phil. thesis, Univ. Oxford (2014)
Home, J. P. et al. Memory coherence of a sympathetically cooled trapped-ion qubit. Phys. Rev. A 79, 050305 (2009)
Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)
Tan, T. R. et al. Multi-element logic gates for trapped-ion qubits. Nature http://dx.doi.org/10.1038/nature16186 (this issue)
Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015)
McDonnell, M. J. et al. High-efficiency detection of a single quantum of angular momentum by suppression of optical pumping. Phys. Rev. Lett. 93, 153601 (2004)
Myerson, A. H. et al. High-fidelity readout of trapped-ion qubits. Phys. Rev. Lett. 100, 200502 (2008)
Acknowledgements
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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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). https://doi.org/10.1038/nature16184
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DOI: https://doi.org/10.1038/nature16184
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