Satellite-to-ground quantum-limited communication using a 50-kg-class microsatellite

Transcription

1 In the format provided by the authors and unedited. SUPPLEMENTARY INFORMATION DOI: /NPHOTON Satellite-to-ground quantum-limited communication using a 50-kg-class microsatellite Hideki Takenaka, Alberto Carrasco-Casado, Mikio Fujiwara, Mitsuo Kitamura, Masahide Sasaki*, and Morio Toyoshima National Institute of Information and Communications Technology (NICT), Nukui-kitamachi, Koganei, Tokyo , Japan. * psasaki@nict.go.jp Recent optical satellite communication demonstrations Optical satellite communications have been demonstrated so far by several missions with satellites larger than SOCRATES, typically several hundred kg, with the lasercom-terminal mass usually over 10 kg. SOCRATES has been the first micro-satellite with a fully-operational on board lasercom system. Other projects based on smaller terminals are being planned as well. Supplementary Figure 1 summarizes the most significant lasercom demonstrations. 1.0E+12 Data rate [bit/s] 1.0E E+06 OSIRISv3 TerraSAR-X OSIRISv2 (2007) (2016) OPTEL-μ LCRD OSIRISv1 LLCD (2013) SOTA (2015) VSOTA ETS-VI (1994) OICETS (2006) SILEX (2001) Planned Space-qualified 1.0E Onboard laser communication terminal mass [kg] Supplementary Figure 1. Comparison of data rates as a function of the on board lasercommunication terminal mass. ETS-VI: Engineering Test Satellite VI; SILEX: Semiconductor-laser Intersatellite Link EXperiment; OICETS: Optical Inter-orbit Communications Engineering Test Satellite; TerraSAR- X: German Synthetic Aperture Radar (SAR) Earth observation satellite; LLCD: Lunar Laser Communications Demonstration; SOTA: Small Optical TrAnsponder; OSIRIS: Optical Space Infrared Downlink System; OPTEL-μ: Optical Terminal for Small Satellite LEO Applications; LCRD: Laser Communications Relay Demonstration. NATURE PHOTONICS Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

2 Clock-data recovery and timing-offset identification Supplementary Figure 2 illustrates an example to understand how to perform the clock-data recovery and timing-offset identification. Suppose we have a received time-tagged photon-count sequence as depicted in Supplementary Fig. 2a, whose duration is over 1.9 s. The thick black arrows represent the signal counts, while the thin red ones represent dark counts. We then choose 10.1 MHz as the candidate clock frequency and divide this sequence into blocks for the corresponding UTI of T = 99 ns. Supplementary Figure 2b depicts the waveform for these blocks. Since the time span of each block is slightly shorter than the clock period (100 ns), the positions of the signal counts, which must appear according to the clock period, deviate in later time, while the positions of the dark counts distribute randomly in the time domain. Finally, we divide the time span of each block into an appropriate bin, which is determined by the time resolution of 1 ns (0.01 UTI), to make a histogram of photon-count events. The histogram should have a sharp peak at around the timing offset if the clock frequency were correctly chosen. We repeated this procedure with various possible UTIs, or equivalently clock frequencies. 2

3 Supplementary Figure 2. Example to illustrate the clock-data recovery and timing-offset identification. a, Received time-tagged photon-count sequence. The thick black arrows represent the signal counts while the thin red ones represent dark counts. b, Waveform blocks for a candidate UTI T. c, Histogram of photon-count events. Supplementary Figure 3 shows an experimental example of the histograms illustrated in Supplementary Fig. 2c taken at 23:59:00 JST (13:59:00 UTC) for a duration of 1 sec on 5 th August 2016, which includes a total of 7119 photon counts. The clock rate and the frequency drift at the OGS which best fitted the received photon-count sequence were identified to be f = 10,000,096.5 Hz and Hz/s, respectively. The timing offset of the click time could also be found to be 0.64 T [sec] in the UTI. As shown in Supplementary Fig. 3, for other choices of clock rates, f-0.3 Hz and f+0.1 Hz, the histograms did not show a sharp peak, meaning that these clock frequencies were wrong. 3

4 Supplementary Figure 3. Experimental example of histograms of received photon-count sequences over unit time interval. Binary sequences related to bit-pattern synchronization Supplementary Figure 4 shows the pattern a as well as the unit sequences which determines this pattern, namely the PN15 sequence, the emission/no-emission (on/off) sequences of Tx2 and Tx3, a 2 and a 3, respectively. Note that a = a 2 + a 3. For the later purpose of cross-correlation calculation, the pattern a is converted into the sequence of -1 and 1, denoted by, by shifting each 0 to a -1. Supplementary Figure 4. Binary sequences related to bit-pattern synchronization. The PN15 PRBS (top), the on/off sequences of a 2 from Tx2 (second top), a 3 from Tx3 (third top), the summed sequence a, and the converted sequence for one period of bits. 4

5 Post-calibration of the quantum receiver. Supplementary Figure 5 shows the configuration of the receiver for the calibration by using the stars. The characteristics of the SPCM channels in the optical link campaign on 5 th August 2016 are summarized in Supplementary Table 1. Supplementary Figure 5. Configuration of the post-calibration of the quantum receiver. Supplementary Table 1. Characteristics of the SPCM channels measured in the optical link campaign on 5th August Detection efficiency Dark count rate Total noise count rate including sky background SPCM1 23% 200 c/s 290 c/s SPCM2 26% 150 c/s 220 c/s SPCM3 46% 150 c/s 160 c/s SPCM4 23% 150 c/s 230 c/s Supplementary Table 2 shows the observed stars at various elevation angles, the input and outputs counts, and the evaluated overall receiver loss in the post-calibration of the quantum receiver. The input counts to the quantum receiver were measured by tapping the star light from the telescope at the entrance of the quantum receiver, and guiding it into an SPCM (not shown in Supplementary Fig. 5). On the other hand, the output counts at each SPCM were measured by directly guiding the star light into the quantum receiver, rotating the linear polarizer over the whole rotation angle of 360. The output counts were then averaged over the whole rotation angle. The overall 5

6 quantum receiver losses could then be evaluated at various elevation angles, and be used for the calibration chart. As a typical value of the quantum receiver loss, we used db for the elevation angles for 53 ~55, for which polarization-reference frame synchronization and QBER estimation were carried out. Supplementary Table 2. Star observation results for post-calibration of the quantum receiver. Date Time Star Input counts to Averaged The overall Telescope the quantum output counts quantum elevation receiver at each SPCM receiver loss [deg] entrance [c/s] [c/s] [db] 2016/12/2 21:30 Capella 59 1,186,253 7, /12/14 19:20 Capella ,514 10, /12/14 19:40 Bellatrix 30 21, /12/14 20:15 Mirfak ,574 4, /12/14 20:40 Deneb 26 3, Supplementary Figure 6 shows an example of the data set acquired from the observed star, Capella, which has almost the same telescope elevation angle as that of the campaign period for 22:59~23:00 on 5 th August 2016, in the post-calibration of the quantum receiver. As seen in Supplementary Fig. 6a, there is the large difference in the SPCM counts of the four polarization channels in the quantum receiver, although the detection efficiencies of SPCM themselves are within 23% ~ 46%. This is due to residual misalignment of optical beam axis in the quantum receiver. Such misalignment should ideally be adjusted by a careful tuning and may be performed with additional optical components. Unfortunately, however, the alignment of the receiver was not optimal because the quantumlimited communication experiment was carried out in parallel with other experiments within the SOTA mission. Moreover, the quantum receiver had been implemented in a compact package, which made it difficult to adjust optical misalignment by using additional optics in the quantum-limited communication experiments using SOTA. This low flexibility in the quantum receiver should be revised in future experiments. Such an imbalance between the detection channels should be compensated in the actual QKD protocol, because it would leave a risk of side-channel attacks. Usually additional attenuators are installed in front of the detectors with higher efficiencies to balance the effective detection efficiencies. This, on the other hand, introduces further losses, reducing the signal count rate. In our experiment, we can effectively emulate this procedure by renormalizing the count rates by that of the channel with the minimum count rate, as shown in Supplementary Fig. 6c. Then the typical value of the quantum receiver loss was reduced from db to db. 6

7 Supplementary Figure 6. Example of the data acquired from the star, Capella, in the post-calibration of the quantum receiver. a, Photon counts of four SPCMs as functions of the polarizer s angle. b, Sinusoidal fitting results of SPCM counts. c, Normalized four SPCM-count values with the highest count value. Calculation of the received polarization angle The predicted linear-polarization angle received at the OGS shown in Fig. 4 in this article was calculated considering the set of information on the SOCRATES orbit, and the reference frames of SOCRATES and SOTA shown in Supplementary Fig. 7: (1) the SOCRATES orbital information during the quantum experiment, which defines the SOCRATES velocity vector; (2) the SOCRATES attitude within the orbit, which defines the SOCRATES reference-frame; the position and the orientation of the SOTA gimbal in SOCRATES, which defines the SOTA reference-frame; and (3) the azimuth and elevation of the SOTA gimbal necessary to track the OGS, which defines the laser-beam vector joining the SOTA reference-frame and the OGS reference-frame. The rotation of these two reference frames along the laser-beam vector defines the rotation of the Tx2/Tx3 received linear-polarization angle. 7

8 Supplementary Figure 7. SOCRATES orbit and the configuration of the reference frames of SOCRATES and SOTA, considered in the calculation of the predicted received polarization angle. Quantum bit error rate Supplementary Table 3 shows the observed transition statistics N(y x). The inputs x=0, 1, are encoded into binary non-orthogonal quantum states, i.e., H- and -45 -polarization states, which are emitted from Tx2 and Tx3, respectively, in SOTA. The outputs from the quantum receiver for the QBER evaluation interval of 12 sec (22:59:21~22:59:33) on 5 th August 2016, denoted as y=0, 1, and F, correspond to the clicks at (i) SPCM3 for y=0, (ii) SPCM2 for y=1, and (iii) SPCM1 or SPCM4 for y=f. Note that some non-integer values appear in Supplementary Table 3. This is because the raw count numbers from each SPCM, which were integer values, were calibrated with the calibration chart to compensate the relative sensitivity of each port for various telescope elevation and azimuth angles. 8

9 Supplementary Table 3. The observed photon-count statistics for each input from Tx2 and Tx3. The transition statistics N(y x) were calculated from the values in this table. Input Tx2 (x=0) Tx3 (x=1) Output (c/s) Output (c/s) JST SPCM1 SPCM2 SPCM3 SPCM4 SPCM1 SPCM2 SPCM3 SPCM4 (y=f) (y=1) (y=0) (y=f) (y=f) (y=1) (y=0) (y=f) 22:59: :59: :59: :59: :59: :59: :59: :59: :59: :59: :59: :59: :59: