Experimental verification of the feasibility of a quantum channel between Space and Earth

Extending quantum communication to Space environments would enable to perform fundamental experiments on quantum physics as well as applications of quantum information at planetary and interplanetary scales. Here, we report the first experimental implementation of a scheme for single-photon exchange between a satellite and an Earth-based station. We built an experiment that mimics a single photon source on a satellite, exploiting the telescope at the Matera Laser Ranging Observatory of the Italian Space Agency to detect the transmitted photons. Weak laser pulses, emitted by the ground-based station, are directed towards a satellite equipped with cube-corner retroreflectors. These reflect a small portion of the pulse, with an average of less-than-one photon per pulse directed to our receiver, as required for the faint-pulse quantum communication. We were able to detect returns from satellite Ajisai, a low-earth orbit geodetic satellite, whose orbit has a perigee height of 1485 km.


Introduction
Free-space quantum communication 1,2 , with fixed transmitter and receivers, has been successfully implemented, with links at increasing distances [3][4][5][6][7][8][9] , reaching 144 Km in a recent experiment 10 . However the extension to even longer distances, in order to perform global-scale distribution of secret keys, or fundamental quantum mechanics experiments, is problematic due to the fact that the long-distance propagation of the optical beam is affected by several atmospheric and geographical hurdles. The most critical issues are wavefront distortion due to atmospheric turbulence, the stability of the optical systems against environmental vibrations and the quality of the large optics needed to mimize the diffractive spreading of the beam diameter. Further constraints follow from Earth's geography (curvature, orography, obstacles, etc.), and from the absorption of radiation in the lower layers of the atmosphere. Since the portion of atmosphere crossed by photons in a Zenith pass corresponds to an equivalent horizontal path of only 8 km at sea-level, we may note that orbiting satellites equipped with quantum terminals could overcome many of the above difficulties, establishing quantum communication links with ground-based stations on arbitrary locations around the Globe 11-18. Here we report the experimental investigations on the exchange of single photons between a low Earth orbiting (LEO) transmitter based on a laser-ranged satellite and a ground-based receiver. These systems have been devised for geodynamical studies and are used to monitor the Earth's gravitational field by means of a series of measurements of the round-trip time (range) of an optical pulse from a station on Earth and the retroreflectors on the satellites 19 . This technique is known as Satellite Laser Ranging (SLR). We took advantage of the fact that their trajectories can be predicted in real time with good precision thanks to very accurate modeling based on their previous passes observed by the International Laser Ranging Service (ILRS) 20 network. 4 In our experiment we simulated a single photon source on a satellite using the retroreflection of a weak laser pulse from a SLR satellite: we chose the relevant experimental parameters in order to bring the number of photons per laser pulse in the downward link much less than unity. Our investigation differs with respect to the SLR techniques, even when the latter reaches the single-photon regime as in the case of Moon laser-ranging or kHz SLR 24 , since we are counting the returns in a series of predetermined time bins and not measuring the range time. Our observable is not the range itself but the number of detected photons per second, the detector count rate (DCR), as an initial step towards the measurement of the individual photons in quantum communication.
Our aim is to demonstrate that a source corresponding to a single photon emitter on a LEO satellite can indeed be identified and detected by an optical ground station, against a very high background noise, comparing the response for different satellites at different distances from the Earth surface.

Scheme of the experiment
The scheme of the ground setup is shown in Fig 1 and consists of a source equipped with a pulsed laser (wavelength 532 nm, repetition rate 17 kHz, energy per pulse 490 nJ and duration of 700 ps) installed along the Coudè path of the 1.5 m telescope of the Matera Laser Ranging Observatory (MLRO) 21 of the Italian Space Agency ASI, located in Matera, Italy. The pulse is directed toward the satellite (Uplink), as indicated in Fig.   2. The portion of the radiation retroreflected into the field-of-view (FOV) of the telescope (Downlink) constitutes the single-photon channel. The key point in the experiment is the use of weak pulses, whose energy is significantly lower than that of the MLRO (100 mJ) as well as the other known SLR sources 25 . In this way, by means of 5 the link budget calculations we can assess that the down link is indeed in the singlephoton regime, which mimics a satellite quantum communication source.
In our experiment an arbitrary polarization state of the photons cannot be preserved, due to multiple reflections along the optical path as well as the backreflection by the satellite 18 : only a dedicated source, with active polarization tracking and control would allow to use the polarization state of the transmitted photons for quantum communication purposes. However, the circular state of polarization is preserved in will be flipped to the orthogonal circular state under reflection. Therefore the circular polarization is used to separate the outgoing from the incoming light beam.
In order to properly track the satellite, it was first acquired and tracked by the MLRO original laser ranging system. The range values were measured using its strong laser pulses (with a repetition rate of 10 Hz, wavelength 532 nm, pulse energy 100 mJ).
After several tens of seconds of successful SLR tracking, the telescope optical path was switched onto the quantum-channel system by moving a motorized mirror into the beam, while the telescope continued to follow in open loop the satellite along its trajectory. The quantum-channel system was kept active for an interval of a few minutes, and then the configuration was switched back to the MLRO system, in order to check the satellite tracking status and to perform further laser-ranging measurements.
Typically, two or more alternations between the MLRO ranging system and our quantum channel were done during each pass of the satellite. Ref. 27 provides further details, including the optical design and detector characteristics of our quantum receiver/transmitter.

Estimating the satellite link budget
The expected detector count rate DCR for the different satellites were calculated according to Degnan radar link equation 23 where the various experimental parameters are defined in Table 1, based on the data for the Ajisai satellite obtained from the ILRS database 26 .
We modeled the link losses and expected detector rates for the satellites under investigation, and the results are listed in Table 2. From this table it is evident that for all satellites we are in the quantum regime, in the sense that the number of photons in the channel per laser shot is much less than one. However there is a large difference in the expected count rates from the different satellites, making Ajisai the best choice for establishing the link according to our needs.
The geodetic satellites considered for our experiment were the most visible ones from MLRO: Ajisai (perigee height of 1485 km), Lageos II (5625 km), Topex-Poseidon (1350 km) and Beacon-C (927 km). The number and type of the retroreflectors as well as the orbits vary significantly among these satellites, leading to different expected optical responses, among which that of Ajisai has the most favourable one.

Adaptation of MLRO system for quantum communication
Since the very nature of our experiment is to analyze a train of single photons as compared to the standard timing analysis of usual SLR, we had to adapt the MLRO system for our requirements. To discriminate the photons belonging to the single photon link reflected by the satellite, from the large number of background photons entering the receiver, the incoming beam was filtered with respect to direction, wavelength and polarization of the incoming beam, and photons time of arrival. 7 For the directional filtering, the design of the FOV has to mediate between different requirements: on one hand it is desirable to narrow the field in order to reduce the amount of background, which scales with the subtended solid angle. On the other hand, an appropriately large FOV is necessary to account for the varying arriving angle of the single photons with respect to the outgoing beam due to velocity aberration 28 , and to the blur due to atmospheric fluctuations and the pointing noise of the telescope. We found that the optimal FOV value for our experimental conditions was 30 arcseconds.
In order to maximize the rejection of the spurious light, an interference band-pass filter with large angular acceptance was used. Moreover, a low-scattering Glan polarizer and a quarter wave plate were also used, in order to cross the polarizations of the up-and down-ward beams. This indeed results as the optimal choice for the rejection of the background photons and good contrast in the calibrations. was derived by the best available information for the satellite pass. 8

Analysis of the detection events
All detection events were correlated with the transmitted laser pulses: for each detection event time stamp t ret , the deviation D from the expected return time t exp , D = t exp -t ret was then computed. These D values, grouped in several bins ∆t of varying width (from 1 to 20 ns), were accumulated over short arcs of the total satellite pass.
According to our criteria, the evidence of the single photon link would have been provided by a statistically significant peak (higher than 3 standard deviations σ of the D value distribution) centred at D = 0. Furthermore, this peak had to persist in the histograms for various values of ∆t, to prove that it was not a statistical artefact of the histogram.
A peak in the returns' histograms satisfying both conditions was identified for the Ajisai pass, see Fig 3, in the time interval 11-16 s after the start of acquisition. The peak is centered at D = 0, as required, and is nearly 5σ above the mean. Moreover, the peak remains well above the statistical limit of 3 standard deviations σ even when analyzing the data with various time bins ∆t between 3 to 19 ns, as shown in Fig. 4. Its statistical significance is at its highest value for ∆t = 5 ns. This value nicely confirms our expectation: the lower side is set by the addition of the instrumental jitters, the higher side by lowering the S/N ratio for accepting a higher spurious background at large bin sizes.
Therefore, the statistical significance of this peak is clearly established. The measured count rate in the peak is 5 counts per second, corresponding to a probability to detect a photon per emitted laser pulse of 3x10 -4 . Taking into account the losses due to detection efficiency (-10dB) and the losses in the detection path (-11dB), the average photon number per pulse, µ, emitted by the satellite and acquired by our detector is approximately 4x10 -2 , i.e. well within the single photon regime. Earth's gravity anomalies, which introduce rapid variations of the range value as high as 100 ns. Therefore, the time delay between emission and arrival times is a rapidly changing and difficult to model quantity, but its proper determination is of crucial importance for the realization of a quantum channel. Accordingly, we expected that the best signal to noise ratio could be achieved for bin sizes ∆t from 1 to 20 ns, and this expectation was confirmed by the subsequent analysis.

Results and Conclusions
According to our statistical analysis, we have been able to detect returned