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Abstract
Free-space quantum key distribution (QKD) is important to realize a global-scale quantum communication network. However, performing QKD in daylight against the strong background light noise is a major challenge. Here, we develop the stochastic parallel gradient descent (SPGD) algorithm with a deformable mirror to improve the signal-to-noise ratio (SNR). We then experimentally demonstrate free-space QKD in the presence of urban daylight. The final secure key rate of the QKD is 98∼419 bps throughout the majority of the daylight hours.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
By exploiting the fundamental principles of quantum mechanics, quantum key distribution (QKD) can theoretically send secure key information between two remote parties, Alice and Bob [1]. Free-space QKD is desired for long-distance applications such as global quantum communication networks via satellites. In the past decade, free-space QKD has been markedly developed on the ground over large distances [2–5], and its systems have become increasingly practical and compact [6–10]. In 2016, China launched the world’s first quantum science satellite dedicated to performing a series of experiments on quantum communication and testing fundamental questions in quantum mechanics [11–13]. The experimental results showed that satellite-to-ground QKD is practical. In the future, it will be possible to place a mobile receiving device for conveniently exchanging secure keys in different locations, including urban environments.
Performing free-space QKD in daylight is a significant barrier to achieving real-life applicability of QKD. A stable free-space channel for QKD requires a high signal-to-noise ratio (SNR). However, the SNR is mainly degraded by optical background noise and atmospheric turbulence [14–17]. Coupling the signal light to a single-mode fiber (SMF) is challenging in an environment with rapidly changing atmospheric turbulence, and sunlight results in additional optical background noise.
Last year, in pursuit of a global real-time quantum communication network based on a quantum satellite constellation, an experimental free-space QKD with a channel loss of at least 40 dB was performed in daylight near Qinghai Lake, China [18]. A free-space working wavelength of 1,550 nm, which is a relatively weak wavelength in the solar spectrum, was selected. Further, the spectral filtering in the up-conversion detectors was strengthened, and spatial filtering with SMF coupling was developed to reduce the noise. However, the available daylight time was very short (15:30∼17:00 local time) [18].
Here, based on the above technologies, we further develop an adaptive optics method to improve the coupling efficiency from free-space to SMF. We firstly use the technique of adaptive optics in urban daylight QKD. A deformable mirror with the stochastic parallel gradient descent (SPGD) algorithm is adopted. Concurrently, we use time-division multiplexing measurement to economize the detector resources. An 8 km QKD experiment is demonstrated over 7 hours throughout daytime via an intracity free-space link in Shanghai, China. Our results show a significant enhancement in the robustness of free-space daylight QKD.
2. Experimental implementation
2.1. Experimental setup
The 8 km free-space QKD experiment was implemented in Shanghai, and the bird’s-eye view of the experiment is shown in Fig. 1. Alice is located at Lane 330, Jiangwen Road (N31°4′5″, E121°32′27″), in Minhang District. Bob is located at Lane 68, Xiuyan Road (N31°8′6″, E121°31′52″), whereas the detectors are located at No. 99, Xiupu Road(N31°7′35″, E121°32′33″), in Pudong New Area. The receiving telescope and the measurement system are in different locations and are connected via a 2 km underground fiber. Such a star-type structure will be suitable for establishing a satellite-to-ground quantum communication network in the future. Different users can obtain secure key via a satellite by sharing a common ground station. By this way, the consumption of ground station resources can be reduced.
Fig. 1 Alice and Bob are located in urban area of Shanghai. The receiving telescope and the measurement system are connected via a 2 km underground fiber. Map data: Google, Digital Globe.
Alice used an integrated telescope including a tracking system as an optical transmitting antenna. A 254-mm aperture Schmidt−Cassegrain telescope made by the Meade Instruments Corporation was used. The primary and secondary mirrors are spherical reflectors which lead to a spherical aberration. A high-order aspheric Schmidt corrector plate was used to correct the spherical aberration. In addition, a tailored eyepiece was used to send laser beams to reduce the chromatic aberration introduced by the transmission Schmidt corrector plate. We used 70X beam expansion to reduce the divergence angle, and the optical transmitting antenna was carefully aligned. In addition, we adjusted the telescope according to the temperature change. As a result, we achieved a near-diffraction-limited far-field divergence angle of approximately 15 µrad.
True single photons emitted from quantum dots and nitrogen-vacancy centers have been used as single-photon sources in proof-of-principle QKD experiments. Herald single photon sources from parametric down-conversion sources are also widely used in quantum communication. However, to benefit from decoy-state methods, weak coherent lights with a higher efficiency and more mature technologies were used in our demonstration. The sending terminal used a 1,550 nm light source with a decoy scheme. At a clock frequency of 100 MHz, the source randomly generated one of four polarization states. The states were |H〉, |V〉, |+〉 and |−〉, with one of three average photon numbers per pulse. The average photon numbers of the signal, decoy and vacuum states were 0.6, 0.2, and 0 per pulse with a probability of 2:1:1, respectively. All random control signals were generated via a high speed random number generator (RNG), as shown in Fig. 2(b).
Fig. 2 Schematic diagram of experimental set-up. (a) The transmitter and receiver terminal are carefully aligned. The divergence angle of the transmitter telescope is 15µrad. The 8 km free-space turbulence link extends across urban areas of Shanghai. 671 nm and 810 nm are beacon lasers. 1,550 nm is the QKD signal light with a decoy scheme. 1,570 nm is for the adaptive optics. The computer connects photoelectric detector and deformable mirror by cable. BS, beam splitter; FSM, fast steering mirror. (b) Controlled by random number generator (RNG), four 1,550nm laser diodes (LDs) are internally modulated to generate four polarization states (|H〉, |V〉, |+〉, |−〉), combined by two fiber polarizing beam splitters (PBSs) and one fiber beam splitter (BS). The LD generates signal with about 2 ns FWHM. LDD, laser diode driver. (c) 1 m delay fiber for time-division multiplexing. PC, polarization controller; SPD, single photon detector.
Stability of beam direction is necessary in free-space QKD experiments. In urban environments, the transmitting and receiving telescopes need to be installed on tall buildings to establish an optical link. In order to realize a successful communication, Alice and Bob were installed with an acquiring, pointing and tracking system that resists the fluctuation effects caused by mechanical deformations in the equipment, atmospheric turbulence, and other adverse impacts. Alice points her beacon laser (810 nm) toward the receiver (Bob). Simultaneously, Bob points his beacon laser (671 nm) back toward Alice, as shown in Fig. 2(a). The CCD camera on Alice’s side detects the incoming beacon laser from Bob. Tracking was achieved using a fast steering mirror (FSM) driven by piezo ceramics. The tracking system shared the same optical path as the quantum channel and was later separated using a dichroic mirror. The final tracking accuracy over the 8 km free-space link was approximately 2.5 µrad. In practice, the FSM can be considered to be part of the adaptive optics system, which can effectively correct lower-order tilt aberrations introduced by the atmosphere.
Bob received photons through a 400 mm-diameter telescope. Conventional free-space optical communication uses low-absorption atmospheric spectral windows in the near-infrared regions of 810 nm and 1550 nm. Our system used 1,550 nm for the QKD and 1,570 nm for a adaptive optics method with a deformable mirror to improve the coupling efficiency to the SMF. After adjusting the entire system, the total channel loss of the 8 km QKD in the urban daylight ranged from 40 dB to 65 dB (the SMF coupling efficiency, atmospheric transmission, and fixed attenuation are 13∼30 dB, 10∼18 dB, and 17 dB respectively).
A schematic of the SPGD control loop is shown in Fig. 2(a). The 1,570 nm light is collected by a SMF and converted into an electrical signal via a photoelectric detector. The computer reads the data from the data acquisition card and executes the SPGD control program. This program controls the deformable mirror to maximize the coupling efficiency at 1,570 nm and 1,550 nm. The 1,550 nm and 1,570 nm lasers are separated by a dense wavelength division multiplexing (DWDM) fiber. At the 1,550 nm output port of the DWDM, we assembled an integrated measurement system consisting of two fiber beam splitters (BSs), a fiber polarization beam splitter (PBS) and two ultralow noise up-conversion single-photon detectors at the telecommunication bands [19]. In the up-conversion single-photon detector modules, we used a narrow-bandwidth volume Bragg grating (VBG) with full-width at half-maximum (FWHM) of 0.05 nm to reduce the noise. With the integrated measurement system, photons coupled in the SMF were detected by single-photon counting modules with average dark counts of 100 Hz. We used a fiber BS to select the measurement basis. A fiber PBS together with two up-conversion SPDs were used for detection. All detected signals were sent to a time-to-digital converter for analysis.
We adopted time-division multiplexing to economize the detector resources [2]. In the QKD experiment, we employed a 1-m long delay fiber to distinguish the different bases, as shown in Fig. 2(c). |H〉 photons and |V〉 photons pass through an extra 1-m long fiber. The arriving time for |H〉 photons and |V〉 photons is 5 ns later than that for |+〉 photons and |−〉 photons. The signal photons go through the 2-km long SMF to the detectors. We used two detectors to distinguish the four polarization states. The advantage of time-division multiplexing is that it reduces the consumption of detectors. However, the disadvantage is the extra 3 dB of attenuation. Time-division multiplexing is a way to save on costs, which benefits the promotion of a practical QKD network.
2.2. SPGD algorithm for single-mode fiber coupling efficiency
There are two types of adaptive optics: conventional adaptive optics and adaptive optics without wavefront detection. Conventional adaptive optics is usually used in imaging systems that are widely applied in astronomical observations. Astronomical observations usually occur at night under conditions of weak turbulence. It is difficult to use adaptive optics to correct laser beams propagating over horizontal atmospheric propagation paths near the ground. Conventional laser beam projection systems that use adaptive optics wavefront shaping with deformable mirrors are not efficient under strong scintillation conditions [20]. Conversely, adaptive optics systems without wavefront detection are simply constructed, have a lower cost, iterate faster and are applicable to various scenarios [21]. Due to these advantages, adaptive optics systems without wavefront detection are more suitable to decrease the influence of atmospheric turbulence. Of the available optimization methods, the SPGD algorithm performs very well, and atmospheric mitigation using SPGD control has been demonstrated in the past [22]. In our study, an adaptive optics system without wavefront detection is used for the free-space QKD to improve the coupling efficiency.
In our system, even though the chromatic aberrations are reduced at the terminals, there are still chromatic aberrations in free-space. A large difference in wavelength might degrade the performance of the adaptive optics. We selected an additional 1,570 nm laser, which is close to the signal light, for the adaptive optics. The coupled power is used as the objective function for the SPGD algorithm. We adopted a photoelectric detector to measure the received 1,570 nm power. The photoelectric detector output signal is used as the performance metric, J. The Voltage J is proportional to the coupled 1,570 nm power. The coupling power of the SMF was optimized by maximizing the photoelectric detector output metric J using the SPGD algorithm [20–24]. The optimization formula is given by
where α is the gain coefficient, n is the number of iterations, is the control voltage matrix of the deformable mirror, and is a set of 144 small-amplitude random control voltage diversifications that perturb the deformable mirror. We set the gain coefficient α to 1. The voltage diversification is 0.2 V or −0.2 V. Between two successive updates of the control voltages on the deformable mirror, the voltage that optimizes the coupling efficiency of the SMF was maximized by sequentially applying a positive perturbation voltage and a negative voltage perturbation and measuring their respective photodetector outputs and .In our experiment, the SPGD control iterates at approximately 1.3 kHz. Prior to the QKD experiment, we carefully aligned the receiving terminal indoors. The performance of the SPGD algorithm during a receiver adjustment is shown in Fig. 3. The SPGD optimization converges and remains stable when we adjust the receiver in the laboratory. In addition, a series of indoor experiments including thermal disturbances and ventilator perturbations were conducted to check the stability. We achieved convergent optimization in these disturbance tests. During the QKD experiment, optimization of the SPGD algorithm control of the deformable mirror was also observed. However, the SPGD optimization did not converge because of the rapidly changing urban atmospheric turbulence. Most of the time, J increased two to three times. By maximizing the photoelectric detector outputs J with the SPGD algorithm, we can maximize the signal strength of the free-space QKD. However, sometimes, there is no obvious improvement of the SMF coupling efficiency because of strong atmospheric turbulence. Fortunately, atmospheric turbulence for satellite-to-ground QKD is weaker than that for horizontal atmospheric propagation paths. The performances of satellite-to-ground optical communications have been greatly improved via the adaptive optics [25]. This study represents an effective attempt to optimize QKD in urban daylight. In the future, adaptive optics will provide an effective method to optimize satellite-to-ground QKD experimental performances.
Fig. 3 Performance of SPGD algorithm during calibration. The curve shows the SPGD optimization process. The photoelectric detector output metric J increases until the SPGD optimization converges.
3. Result
Aided by the SPGD algorithm and the deformable mirror, we improved the SMF coupling efficiency of the QKD over the 8 km turbulent channel. The 8 km free-space QKD experiment was implemented throughout most of the daylight hours. The final secure key was extracted from the raw data by a standard decoy BB84 post-processing procedure [26, 27]. The final key rate was obtained as
where q = 1/2 is the basis reconciliation factor, pµ is the probability of emitting signal states, Qµ and Eµ denote the gain and error rate of the signal states, respectively, and f is the error correction efficiency. The errors were corrected by low-density parity-check code. H2(e) = −elog2(e) − (1 − e)log2(1 − e) is the binary Shannon entropy function, and Q1 is the gain when the source generates single-photon states.After these adjustments, the QKD operated successfully over the 8 km link throughout most of the day. This result demonstrates the feasibility of long period satellite-to-ground QKD during daylight hours. By correcting the optical aberrations, the deformable mirror with the SPGD algorithm achieved QKD even in a high-loss channel. Finally, we achieved long period QKD during urban daylight (see Fig. 4). The experimental parameters are listed in Table 1. In our experiment, the error correction efficiency f is 1.1. The experiment was performed on a sunny to cloudy day. The quantum bit error rate (QBER) of the signal states was 1.97% ∼ 3.44%. The final secure key rate was 98 ∼ 419 bps throughout most of the daylight hours. We successfully performed the QKD experiment from 7:00 to 9:00, and from 14:00 to 19:00. The implementation of the free-space QKD was therefore greatly extended in urban daylight; however, it failed between 10:00 and 13:00. The turbulence intensity is always high in the middle of the day [28, 29], leading to a low coupling efficiency. Moreover, bright sunlight results in stronger optical background noise near noon. Therefore, implementing a free-space QKD experiment in the middle of the day is still extremely difficult. We made an effective attempt to extend the time available to implement QKD in urban daylight; however, there is still room for improvement including optimizing the adaptive optics, developing more advanced filtering techniques and adopting a better detection system.
Fig. 4 QKD experimental result over the 8 km free-space turbulent link across an urban area of Shanghai. The failure between 10:00 and 13:00 is attributed to the low coupling efficiency of the SMF and the large amount of background noise.
Table 1. Parameters for the QKD experiment. Qµ and Qν are the gains for the signal states and decoy states, respectively. Y0 is the yield for vacuum states. Y1 is the yield when the source generates single-photon states. Eµ and Eν are the QBERs of the signal states and decoy states, respectively.
4. Conclusion
We experimentally demonstrated 8 km free-space daylight QKD in the city of Shanghai. By developing an adaptive optics system using a deformable mirror and the SPGD algorithm, we successfully improved the SMF coupling efficiency. In addition, we adopted a time-division multiplexing measurement to economize the detector resources. The final secure key rate in our experiment was 98 ∼ 419 bps throughout most of the daylight hours. The experimental result indicates that it is feasible to achieve long-distance free-space QKD in urban daylight with efficient adaptive optics technology. This study greatly enhanced the robustness of free-space daylight QKD. In the future, satellite-to-ground QKD will be an indispensable component to achieve a global quantum key network, and adaptive optics will be an effective method to optimize satellite-to-ground QKD.
Funding
National Natural Science Foundation of China (under grant No.11405172 and No.11654005); Anhui Initiative in Quantum Information; Youth Innovation Promotion; Shanghai Sailing Program (No.18YF1425100).
Acknowledgments
We acknowledge D.-D. Li, X. Han, H. Dai, B. Li, Z.-P. Li, Q.-M. Lu and H.-B. Xie for their helpful discussions during the course of this article.
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