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On-chip generation of high-dimensional entangled quantum states and their coherent control


Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science1. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics2, for increasing the sensitivity of quantum imaging schemes3, for improving the robustness and key rate of quantum communication protocols4, for enabling a richer variety of quantum simulations5, and for achieving more efficient and error-tolerant quantum computation6. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states7. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2)8,9,10,11. Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.

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Figure 1: Experimental setup for high-dimensional quantum state generation and control.
Figure 2: Characterization of the quantum state dimensionality.
Figure 3: Experimental implementation of the coherent control of frequency-entangled high-dimensional quantum states.
Figure 4: Bell inequality violation and quantum state tomography of frequency-entangled states.


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This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Steacie, Strategic, Discovery and Acceleration Grants Schemes, by the MESI PSR-SIIRI Initiative in Quebec, by the Canada Research Chair Program and by the Australian Research Council Discovery Projects scheme (DP150104327). C.R. and P.R. acknowledge the support of NSERC Vanier Canada Graduate Scholarships. M.K. acknowledges funding from the European Union’s Horizon 2020 Research and Innovation programme under the Marie Sklodowska-Curie grant agreement number 656607. S.T.C. acknowledges support from the CityU APRC programme number 9610356. B.E.L. acknowledges support from the Strategic Priority Research Program of the Chinese Academy of Sciences (grant number XDB24030300). B.W. acknowledges support from the People Programme (Marie Curie Actions) of the European Union’s FP7 Programme under REA grant agreement INCIPIT (PIOF-GA-2013-625466). L.C. acknowledges support from the People Programme (Marie Curie Actions) of the European Union’s FP7 Programme under REA Grant Agreement number 627478 (THREEPLE). R.M. acknowledges additional support by the Government of the Russian Federation through the ITMO Fellowship and Professorship Program (grant 074-U 01) and from the 1000 Talents Sichuan Program. We thank R. Helsten and M. Islam for technical insights; A. Tavares, T. Hansson and A. Bruhacs for discussions; T. A. Denidni and S. O. Tatu for lending us some of the required experimental equipment; P. Kung from QPS Photronics for help and the use of processing equipment; as well as Quantum Opus and N. Bertone of OptoElectronics Components for their support and for providing us with state-of-the-art photon detection equipment.

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Authors and Affiliations



C.R. and M.K. developed the idea and contributed equally. C.R., M.K., P.R., L.R.C., B.W. and Y.Z. designed the experiment, performed the measurements and analysed the experimental results. S.S. and L.C. led the theoretical analysis. B.E.L. and S.T.C. designed and fabricated the integrated device. A.C. and D.J.M. participated in scientific discussions. R.M. and J.A. supervised and managed the project. All authors contributed to the writing of the manuscript.

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Correspondence to Michael Kues or Roberto Morandotti.

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Extended data figures and tables

Extended Data Figure 1 Bell inequality violation for frequency-entangled states after propagation through a 24.2-km fibre system.

To show that frequency-entangled states can be used towards quantum communication schemes, we sent the signal and idler photon each through 20 km of standard telecommunications fibre followed by a 4.2-km-long dispersion-compensating fibre. For D = 2, we measured (by tuning the relative phase θ between each frequency bin of the signal and idler photon) a variation in coincidence counts (red crosses) with a quantum interference visibility V2 of 79.8% (violating a Bell inequality for D = 2), thus demonstrating that entanglement was maintained over this distance (the black curve being the recorded background). Source Data for this figure is available online.

Source data

Extended Data Figure 2 Coherent mixing of multiple frequency modes.

D modes (here, D = 2, 3 or 4) are spectrally selected (solid black line) (any mode ) and mixed (red arrows) by means of an electro-optic phase modulator. The frequency mode where all components overlap (red dashed line) is then selected via a narrow spectral filter (blue dashed window). For D = 2 and 3, a frequency shift of 200 GHz (equal to the FSR) is implemented, whereas for D = 4 two different frequency shifts of 100 GHz (equal to 1/2 FSR) and 300 GHz (equal to 3/2 FSR) are enforced. In all cases, this is achieved through sideband generation. Note that for D = 4, and in contrast to D = 2 and 3, the final frequency mode does not overlap with any microcavity resonance.

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Kues, M., Reimer, C., Roztocki, P. et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622–626 (2017).

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