1.
2.
3.
4.
Methods
Two-photon comb. Two photons were generated by the SPDC process in two
PPLN crystals (manufactured by Jinan Institute of Quantum Technology) having
the dimensions of 0.5 × 3 × 10 mm and 0.5 × 0.5 × 10 mm, arranged orthogonally in
a bow-tie cavity. The small dimensions allowed the crystals to precisely align with
the laser path. The temperatures of the crystals and their holders were stabilized to
be within ~1 mK. An SPDC pump laser of 757 nm was obtained by second harmonic generation (SHG) of a 1514-nm external-cavity diode laser (Sacher,
TEC420-1530-1000), whose wavelength was stabilized using acetylene molecules.
The pump laser was focused to a waist size of ~25 μm using lenses and a
plano–concave mirror to achieve strong parametric interaction53.
The optical cavity was stabilized using the Pound–Drever–Hall technique for
this laser with an optical chopper with a duty cycle of 1/3. The two photons were
separated using a 50:50 laser-line beam splitter, following which they entered a
tomographic setup consisting of a zero-order 1514-nm quarter-wave plate, halfwave plate, and vertical-transmittance polarizer, similar to that in ref. 43. To
generate a Bell state, two additional half-waveplates were placed in the path of one
photon: one plate was used as a phase shifter by aligning the yaw angle, and the
other was used as a bit flipper with a slow axis of 45°. The measurement time for
one basis was 15 s, which was sufficient to converge the correlation function with a
relatively strong pump power of 100 μW. The total testing time was ~10 min,
including a rest time of 20 s. In almost all our experiments, the SSPDs were
superconducting single-photon detectors with a detection efficiency of ~85%,
which was the maximum value for our setup. However, a detection efficiency of
~60% was used in the experiments yielding the results shown in Fig. 4b (blue dots)
because our SiAPDs had an efficiency of 60% for visible wavelengths (SPCMAQRH-14-FC). The maximal input power was 10 mW, resulting in a detected
count rate approaching the limit of ~107. We utilized HydraHarp 400 as a TCSPC
module, whose resolution is 32 ps for that shown in Fig. 2a, and 16 ps for the
others. The 32-ps resolution was used because it could record longer interval times,
which was required for measuring the coincidences with an adequate margin.
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Acknowledgements
We thank H. Goto, Q. Zhang, Y. Yamamoto, S. Utsunomiya, T. Kobayashi, M. Fraser, I.
Iwakura, S. Tamura, K. Ikeda, and F.-L. Hong for their support. This work was supported
by the Toray Science Foundation, the Asahi Glass Foundation, the KDDI Foundation,
the SECOM Foundation, Research Foundation for Opto-Science and Technology, JST
PRESTO JPMJPR1769, JST START ST292008BN, and Kanagawa Institute of Industrial
Science and Technology (KISTEC). T.H. also acknowledge members of Quantum
Internet Task Force, which is a research consortium to realize the Quantum Internet, for
comprehensive and interdisciplinary discussions of the Quantum Internet.
Author contributions
K.N. and T.H. conceived this project. K.N., D.Y., I.N., N.T., K.O., and T.H. designed the
experiments. M.-Y.Z. and X.-P.X. fabricated the SPDC crystals. K.N., D.Y., and K.I.
performed the experiments. K.N. and T.H. analyzed the data and drafted the manuscript.
K.N., N.T., X.-P. X., and T.H. revised the text. All the authors contributed to discussions.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s42005020-00406-1.
Correspondence and requests for materials should be addressed to T.H.
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