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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20032–20040
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Experimental quasi-single-photon transmission from satellite to earth

Juan Yin, Yuan Cao, Shu-Bin Liu, Ge-Sheng Pan, Jin-Hong Wang, Tao Yang, Zhong-Ping Zhang, Fu-Min Yang, Yu-Ao Chen, Cheng-Zhi Peng, and Jian-Wei Pan  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20032-20040 (2013)
http://dx.doi.org/10.1364/OE.21.020032


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Abstract

Free-space quantum communication with satellites opens a promising avenue for global secure quantum network and large-scale test of quantum foundations. Recently, numerous experimental efforts have been carried out towards this ambitious goal. However, one essential step - transmitting single photons from the satellite to the ground with high signal-to-noise ratio (SNR) at realistic environments - remains experimental challenging. Here, we report a direct experimental demonstration of the satellite-ground transmission of a quasi-single-photon source. In the experiment, single photons (∼0.85 photon per pulse) are generated by reflecting weak laser pulses back to earth with a cube-corner retro-reflector on the satellite CHAMP, collected by a 600-mm diameter telescope at the ground station, and finally detected by single-photon counting modules after 400-km free-space link transmission. With the help of high accuracy time synchronization, narrow receiver field-of-view and high-repetition-rate pulses (76 MHz), a SNR of better than 16:1 is obtained, which is sufficient for a secure quantum key distribution. Our experimental results represent an important step towards satellite-ground quantum communication.

© 2013 OSA

1. Introduction

In the meantime, besides the experimental efforts in the ground, satellite based quantum communication projects have been proposed by several different countries [8

8. H. Xin, “Chinese academy takes space under its wing,” Science 332, 904 (2011). [CrossRef]

10

10. T. Jennewein and B. Higgins, “The quantum space race,” Phys. World 26, 52–56 (2013).

] and the launching time has been scheduled. Before the launching of the satellite, however, a direct study of the whole process of transmitting and detecting single photons from the satellite to the ground with the help of existing satellite or aircraft at realistic envirments is necessary but remains experimental challenging owing to the high background noise level from all stars and the difficulties of tracking and synchronization.

2. Scheme

As shown in Fig. 1, our experimental system consisted of a tracking and pointing telescope, a high repetition rate laser, a receiving terminal for collecting and detecting single-photons and a data-acquisition system. The telescope employed the binocular structure which could achieve the separation of emitting and receiving photons. The transmitting and receiving telescopes, with diameter of 20 cm and 60 cm respectively, are separated by 30 cm. The main advantage of this structure is that we can modulate the transmitting optical signal, and provide multiple-measurement basis on quantum signal conveniently. On the other hand, in order to realize the independence and synchronization between detecting quantum signal and LRS signal, we located dichroic mirrors (DMs) in both transmitting and receiving optical path.

Fig. 1 The scheme of the single-photon link from satellite to experimental setup installed at the Shanghai Observatory. CHAllenging Minisatellite Payload (CHAMP) was a German satellite launched July 15th, 2000 from Plesetsk, Russia and was used for atmospheric and ionospheric research, as well as other geoscientific applications. It was covered by 2 cm-diameter retroreflectors on each side. A train of pulses of 3 ps duration, 702 nm wavelength, 0.4 nJ of energy and 76 MHz repetition rate are coupled with the LRS pulses before being sent toward the transmitting telescope with aperture of 20 cm. The neutral density (ND) filter is used to control the weak pulse light, and the chopper is used to filter the backscattering noise. After the beam spreading, a fraction of the beam in the uplink path irradiates the satellite CHAMP. The corner cubes on the satellite retro-reflect back to the Earth a small portion of the photons in the laser pulse (downlink), which is the single-photon channel. Some of the photons in the downlink path are collected by the receiving telescope, a reflecting telescope with aperture of 60 cm, and detected by SPCMs, placed behind polarization measurement devices and spectral filters. The transmitting telescope and the receiving telescope are separated by a distance of 30 cm. All relevant events in the time domain are recorded by time measurement system TDC, and then referred to as coordinated universal time.

At the transmitting side, a laser beam (wavelength of 702 nm, repetition rate of 76 MHz, single-pulse energy of 0.4 nJ, and pulse width of 3 ps) was coupled by a dichroic mirror with a green laser beam from the LRS of Shanghai Observatory. Then the coupled beams were transmitted from the transmitting telescope. Due to employment of a laser with high repetition rate, it made a possibility that we can receive enough single-photons coming from the satellites in a few minutes. The neutral density (ND) filter in the transmitting path was used to achieve energy control of the weak light pulse. The chopper was used to wipe out backscattering noise. Obviously, the telescope is composed by a number of mirrors, two of which control the position and height of the telescope. The rotation of the mirrors led to changes in polarization of the incident and the emergent light. An electronic-controlled half-wave plate (EC HWP) was added in the transmitter for polarization tracking.

At the receiving side, an optical detection was installed in the place of an original complementary metal-oxide semiconductor (CMOS). After the light reflected by the satellite enters the receiving telescope, it was focused by a primary and a secondary mirror. A meniscus lens reflected the light whose wavelength was 532 nm to the ocular. Because of the perfect separation of quantum signal and LRS signal, we could operate the complete polarization analysis of the incoming photons which will detected by single-photon counting modules (SPCMs). The transmitting and receiving photoelectric conversion signal would be led into a time-to-digital converter (TDC) and analyzed by a computer.

In this experiment, we have made some improvements to reduce background noise, such as adopting spatial, spectral and time filtering. We test the receiving field-of-view (FOV) of the detection system by scanning the telescope and recording the light intensity of the Polaris. As shown in Fig. 2, we experimentally demonstrated that FOV is 5″. Besides, a narrow band filter with the bandwidth of 3 nm was added to the receiving optical path to filter out background noise (including reflected lights from the sky and the ground) from the desired signal. In addition, we sectioned the transmitted pulsed laser from time sequence and filtered the backscattering by controlling the detection time. Every time after a transmitted laser pulse had passed the aerosphere, determining by the influence of the backscattering from the aerosphere was obviously within 30 km (round trip time of 200 μs), we detected the echo signal and avoided these kinds of noise. Besides, we did our experiment at night and choose the satellite in the shadow of the earth. Thus, even on a clear night we manage to reduce the background noise above the zenith angle of 45° to be less than 100 counts per second (cps).

Fig. 2 FOV of the detection system testing by scanning and recording the light intensity of the Polaris. The telescope was tracked to the Polaris, which could be seen as a fixed star. By changing the relative telescope tracking point, we record the different count rates of the changing position by SPCMs. Fig. 2(a) was the three-dimensional draw according to the counts. Fig. 2(b) was the fitting curve of FOV in the azimuth axial. Fig. 2(c) was the fitting curve of FOV in the zenith axial.The FOV of the receiving system, in both the azimuth and zenith axials, were measured to be less than 5″.

The key experimental parameters were shown in table 1. Here, the pulse energy E was 0.4 nJ; S, the photon number per joule, was 3.53 × 1018 (702 nm); As, the effective area of satellite corner retro-reflector, was 11.34 cm2; Ar, the effective area of receiving telescope, was 0.25 m2 ; Kt was the efficiency of transmission system of 0.2; Kr was the efficiency of optical receiving system of 0.15, including 0.5 for receiving telescope, 0.5 for coherent filter and 0.6 for multimode fiber collection; T was one-way atmospheric transmission of 0.6; η was the quantum efficiency of receiving detection device of 0.65; α was the attenuation factor of 13 dB, including 0.2 for the influence of satellite retro-reflector efficiency, 0.5 for both of atmospheric jitter and turbulence respectively; R was the satellite distance of 400 km for CHAMP; θt was the laser beam divergence angle of 300±15 μrad, as the LRS, where the 5 % uncertainty was mainly due to the temperature change of the environment (the telescope was designed for tracking satellites at different altitude from LEO to GEO, thus the divergence angle is far larger than the telescope’s diffraction limit at 400 km altitude); θs was the diffraction angle of satellite retro-reflector of 38 μrad, which was considered by both the clear aperture of the prism’s front face and the nominal width of the far field peaks given in [12

12. R. Neubert, L. Grunwaldt, and J. Neubert, “The retro-reflector for the CHAMP satellite: Final design and realization,” in Proceedings of the 11th International Workshop on Laser Ranging, (Deggendorf, Germany, 1998), pp. 260–270.

, 13

13. L. Grunwaldt, R. Neubert, and K. Lapushka, “First results of laser ranging to the CHAMP retroreflector,” in Proceedings of the 12th International Workshop on Laser Ranging, (Matera, Italy, 2000).

].

According to the parameters in Table 1, we could calculate the one-way channel attenuation from ground to satellite:
ηup=4AsKtTαπR2θt2=6.00×1010.
(1)
The numbers of photons reflected from satellite was varied between 0.76 to 0.94, corresponding to the uncertainty of divergence angle:
N0=ESηup=0.85±0.09.
(2)
Attenuation in the one-way channel from satellite to earth was:
ηdown=4ArKrTηπR2θs2=8.07×105.
(3)
Therefore, the theoretical number of photons detected by each pulse at the receiving end was:
N=N0ηdown=6.83×105.
(4)

Table 1. Parameters of satellite-to-ground quantum channel link.

table-icon
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3. Result

In our experiment, the effective measurement time of the return signal of the CHAMP satellite (400 km) in each period (τ = 16 ms) of the chopped wave was τ0 = 1.65 ms. For example, the number of echo signals in 10 s was 5385. Thus the average counts per second were N¯=5222. The measured dark counts per second were Nb¯=89. Therefore, the photon number per echo generated by a single laser pulse was experimentally measured:
Nexp=N¯Nb¯Λ=6.75×105
(5)

The repetition rate of the present traditional LRS could be achieved at the magnitude of up to kHz. However, a light source having a higher repetition rate and time resolution was required due to the high loss in the channel. In the time synchronization system of our experiment, the quantum system and the LRS were independent. By this way we got rid of the frequency limitation of the LRS. We also utilized a TDC with high accuracy to record the arrival time of the photons and sample the pulsed photons [14

14. J. Song, Q. An, and S.-B. Liu, “A high-resolution time-to-digital converter implemented in field-programmable-gate-arrays,” IEEE Trans. Nucl. Sci. 53, 236–241 (2006). [CrossRef]

]. After being reflected by the satellite and passing through a 400 km satellite-to-ground link, the photons would be detected. We defined t0 as the emission time and t as the corresponding return time. According to the return time t of each photon, and the real-time satellite distance tc, we could calculate the theoretical transmitting time texp, We used the difference D = t0texp to characterize the accuracy of the time information.

Although the photons were emitted in pulsed intervals, the return time which we detected was disordered due to the changing distance of the satellite. To identify which pulse the photons belong to, we had to take the satellite distance measured by the laser as a synchronization data and obtained the round-trip time deviation by performing of offline analysis. The satellite orbit fitting curve was shown in Fig. 3. The distance of CHAMP satellite we measured in Shanghai Observatory was between 350km to 400km during our records. The histogram of all D values with 0.1 ns as the unit was shown in Fig. 4. The time synchronization accuracy was 1.35±0.03 ns at the full width at half maximum (FWHM). The main factors influencing time accuracy included: 350 ps for the time resolution of SPCMs, 160 ps for the accuracy of TDC, 1000 ps for the fitting precision of satellite orbit, and the rest effect for the time jitter of our pico-second pulsed laser.

Fig. 3 Plot of the range Rs between the satellite CHAMP and Shanghai Observatory. The round-trip time of the signal, directly proportional to Rs, exhibits strong and rapid variations during the satellite passage. The blue points are the LRS system’s records and the red line is the fitting curve on the survey data. The efficient time with maximal counts of single photons reflected from satellite and detected by SPCMs is shown in the gray box. The perigee height of CHAMP satellite that day was about 330km. The distance was ranging from 350 km to 400 km during our records of 15 s.
Fig. 4 Histogram of all D values between expected and observed detections for CHAMP satellite.We summarized the D values numerically with 0.1ns as the unit. The peak of the histogram is centered at 0 ns, as expected. By Gaussian fitting, the full width at half maximum (FWHM) time accuracy was observed 1.35±0.03 ns.

By using 2 ns bin size to deal with the experimental data, we got the effective echo signals counts N¯=1000 and the effective dark counts Nb¯=58. The SNR was calculated as follow:
SNR=N¯Nb¯Nb¯=16.2
(6)

In addition, the long-distance free-space quantum communication usually uses polarization coding. A crucial problem of satellite-to-ground communication was how to realize the polarization coding and basis measurement based on the kinematical reference system. While the satellite reference frame keeps changing during satellites’ motion, the satellite and ground are relatively static when the two sides stare at each other at any specific time in this frame. In our experiment, the reflecting surfaces of the retro-reflector were aluminium (Al) coated [12

12. R. Neubert, L. Grunwaldt, and J. Neubert, “The retro-reflector for the CHAMP satellite: Final design and realization,” in Proceedings of the 11th International Workshop on Laser Ranging, (Deggendorf, Germany, 1998), pp. 260–270.

, 13

13. L. Grunwaldt, R. Neubert, and K. Lapushka, “First results of laser ranging to the CHAMP retroreflector,” in Proceedings of the 12th International Workshop on Laser Ranging, (Matera, Italy, 2000).

]. Ground tests show that depolarization caused by Al coated reflector could not be compensated by unitary polarization transformation due to the different reflectivity on horizontal and vertical polarizations. Fortunately, this spacial problem will not exist in the final design [8

8. H. Xin, “Chinese academy takes space under its wing,” Science 332, 904 (2011). [CrossRef]

]. As a demonstration, in the present experiment we achieve polarization maintaining by utilizing the reference frame.

As the telescope was composed by a number of mirrors, two of which control the position and height of the telescope. The rotation of the reflectors, which indicated by the azimuth and altitude encoder, led to changes in polarization [15

15. C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a space-earth quantum communication link,” Opt. Express 14, 10050–10059 (2006). [CrossRef] [PubMed]

, 16

16. C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009). [CrossRef]

]. The real-time encoder data were used to drive the half-wave plate for polarization tracking. Fig. 5 shows the normalized intensity curve of horizontal and vertical polarization with the rotation of the telescope in the case of with or without polarization tracking. In case of no tracking, it looks like the sine curve. Finally, the maintenance of the polarization under tracking had been tested to be more than 100:1.

Fig. 5 Normalized intensity curve of horizontal and vertical polarization with the rotation of the telescope measured under the reference frame moving with the telescope. With a linearly polarized light incidenting without any compensation, the curve of horizontal (vertical) polarization show a sinesoid, as shown in curve H (V). With the polarization tracking system, the curve H′ and V′ show a nearly constant ratio. The maintenance of the polarization has a extinction ratio better than 100:1.

4. Conclusion and perspectives

Acknowledgments

We acknowledge insightful discussions with Qiang Zhang. This work has been supported by the National Fundamental Research Program (under grant no. 2011CB921300 and 2013CB336800), the Chinese Academy of Sciences and the National Natural Science Foundation of China.

References and links

1.

D. Salart, A. Baas, C. Branciard, N. Gisin, and H. Zbinden, “Testing the speed of ’spooky action at a distance’,” Nature 454, 861–864 (2008). [CrossRef] [PubMed]

2.

J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett. 110, 260407 (2013). [CrossRef] [PubMed]

3.

X.-S. Ma, J. Kofler, A. Qarry, N. Tetik, T. Scheidl, R. Ursin, S. Ramelow, T. Herbst, L. Ratschbacher, A. Fedrizzi, T. Jennewein, and A. Zerlinger, “Quantum erasure with causally disconnected choice,” Proc. Natl. Acad. Sci. 110, 1221–1226 (2013). [CrossRef] [PubMed]

4.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007). [CrossRef] [PubMed]

5.

J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature 488, 185–188 (2012). [CrossRef] [PubMed]

6.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zerlinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012). [CrossRef] [PubMed]

7.

J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photonics 7, 387–393 (2013). [CrossRef]

8.

H. Xin, “Chinese academy takes space under its wing,” Science 332, 904 (2011). [CrossRef]

9.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Fedrizzi, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lutkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-QUEST: Experiments with quantum entanglement in space,” Europhysics News 40, 26–29 (2009). [CrossRef]

10.

T. Jennewein and B. Higgins, “The quantum space race,” Phys. World 26, 52–56 (2013).

11.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys. 10, 033038 (2008). [CrossRef]

12.

R. Neubert, L. Grunwaldt, and J. Neubert, “The retro-reflector for the CHAMP satellite: Final design and realization,” in Proceedings of the 11th International Workshop on Laser Ranging, (Deggendorf, Germany, 1998), pp. 260–270.

13.

L. Grunwaldt, R. Neubert, and K. Lapushka, “First results of laser ranging to the CHAMP retroreflector,” in Proceedings of the 12th International Workshop on Laser Ranging, (Matera, Italy, 2000).

14.

J. Song, Q. An, and S.-B. Liu, “A high-resolution time-to-digital converter implemented in field-programmable-gate-arrays,” IEEE Trans. Nucl. Sci. 53, 236–241 (2006). [CrossRef]

15.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a space-earth quantum communication link,” Opt. Express 14, 10050–10059 (2006). [CrossRef] [PubMed]

16.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009). [CrossRef]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5565) Quantum optics : Quantum communications
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: May 28, 2013
Revised Manuscript: July 19, 2013
Manuscript Accepted: August 5, 2013
Published: August 19, 2013

Citation
Juan Yin, Yuan Cao, Shu-Bin Liu, Ge-Sheng Pan, Jin-Hong Wang, Tao Yang, Zhong-Ping Zhang, Fu-Min Yang, Yu-Ao Chen, Cheng-Zhi Peng, and Jian-Wei Pan, "Experimental quasi-single-photon transmission from satellite to earth," Opt. Express 21, 20032-20040 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20032


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References

  1. D. Salart, A. Baas, C. Branciard, N. Gisin, and H. Zbinden, “Testing the speed of ’spooky action at a distance’,” Nature454, 861–864 (2008). [CrossRef] [PubMed]
  2. J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, “Lower bound on the speed of nonlocal correlations without locality and measurement choice loopholes,” Phys. Rev. Lett.110, 260407 (2013). [CrossRef] [PubMed]
  3. X.-S. Ma, J. Kofler, A. Qarry, N. Tetik, T. Scheidl, R. Ursin, S. Ramelow, T. Herbst, L. Ratschbacher, A. Fedrizzi, T. Jennewein, and A. Zerlinger, “Quantum erasure with causally disconnected choice,” Proc. Natl. Acad. Sci.110, 1221–1226 (2013). [CrossRef] [PubMed]
  4. T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett.98, 010504 (2007). [CrossRef] [PubMed]
  5. J. Yin, J.-G. Ren, H. Lu, Y. Cao, H.-L. Yong, Y.-P. Wu, C. Liu, S.-K. Liao, F. Zhou, Y. Jiang, X.-D. Cai, P. Xu, G.-S. Pan, J.-J. Jia, Y.-M. Huang, H. Yin, J.-Y. Wang, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels,” Nature488, 185–188 (2012). [CrossRef] [PubMed]
  6. X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zerlinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature489, 269–273 (2012). [CrossRef] [PubMed]
  7. J.-Y. Wang, B. Yang, S.-K. Liao, L. Zhang, Q. Shen, X.-F. Hu, J.-C. Wu, S.-J. Yang, H. Jiang, Y.-L. Tang, B. Zhong, H. Liang, W.-Y. Liu, Y.-H. Hu, Y.-M. Huang, B. Qi, J.-G. Ren, G.-S. Pan, J. Yin, J.-J. Jia, Y.-A. Chen, K. Chen, C.-Z. Peng, and J.-W. Pan, “Direct and full-scale experimental verifications towards ground-satellite quantum key distribution,” Nat. Photonics7, 387–393 (2013). [CrossRef]
  8. H. Xin, “Chinese academy takes space under its wing,” Science332, 904 (2011). [CrossRef]
  9. R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Fedrizzi, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lutkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-QUEST: Experiments with quantum entanglement in space,” Europhysics News40, 26–29 (2009). [CrossRef]
  10. T. Jennewein and B. Higgins, “The quantum space race,” Phys. World26, 52–56 (2013).
  11. P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and earth,” New J. Phys.10, 033038 (2008). [CrossRef]
  12. R. Neubert, L. Grunwaldt, and J. Neubert, “The retro-reflector for the CHAMP satellite: Final design and realization,” in Proceedings of the 11th International Workshop on Laser Ranging, (Deggendorf, Germany, 1998), pp. 260–270.
  13. L. Grunwaldt, R. Neubert, and K. Lapushka, “First results of laser ranging to the CHAMP retroreflector,” in Proceedings of the 12th International Workshop on Laser Ranging, (Matera, Italy, 2000).
  14. J. Song, Q. An, and S.-B. Liu, “A high-resolution time-to-digital converter implemented in field-programmable-gate-arrays,” IEEE Trans. Nucl. Sci.53, 236–241 (2006). [CrossRef]
  15. C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a space-earth quantum communication link,” Opt. Express14, 10050–10059 (2006). [CrossRef] [PubMed]
  16. C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys.11, 045017 (2009). [CrossRef]

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