Boosting higher secret key rate in quantum key distribution over mature telecom components


 Secret key rate is a core performance indicator in implementing quantum key distribution, which directly determines the transmission rate of enciphered data. Here we demonstrate a high-key-rate quantum key distribution system over mature telecom components. The entire framework of quantum key distribution over these components is constructed. The high-rate low-noise Gaussian modulation of coherent states is realized by a classical electro-optic IQ modulator. High-baud low-intensity quantum signals are received by a commercial integrated coherent receiver under the shot-noise limit. A series of digital signal processing algorithms are proposed to achieve accurate signal recovery and key distillation. The system has yield a secret key rate of 10.37 Mbps, 1.61 Mbps, 337.82 kbps, and 58.06 kbps under the standard telecom fiber of 20 km, 50 km, 70 km, and 100 km, respectively. Our results represent the achieved highest secret key generation rate for quantum key distribution using continuous variables at a standard telecom wavelength. Moreover, it breaks the isolation between quantum communication and classical optical communication in terms of components, and opens the way to a high-speed and cost-effective formation of metropolitan quantum secure communication networks.


Introduction
Quantum key distribution (QKD), one quantum informa-Specifically, in quantum private communication, information-23 theoretically secure can only be achieved by combining one-24 time-pad (OTP) encryption protocol at a time with QKD. OTP 25 protocol requires the key used only once and be as long as 26 the message, which means that SKR needs to be consistent 27 with the classical data rate. As the communication techniques 28 improve, classical optical communications that provide 100 29 Gbit/s per wavelength channel are deployed 19 . A field trial 30 featuring an aggregate data rate of 54.2 Tbit/s has been carried 31 out 20 . Some alternative protocols, such as quantum stream 32 cipher 21 and physical-layer secret key generation and distri-33 bution (SKGD) 22 , can offer a higher rate, but their security 34 has not been proven entirely yet. Therefore, it is clear that if 35 we want to encrypt high volumes of classical network traffic 36 using OTP in the longer term, significant developments on the 37 SKR generated by QKD are required 18 . 38 In terms of improving the SKR, much work has been done 39 for discrete-variable quantum key distribution (DV-QKD), 40 such as improving the repetition rate to gigahertz 23 , develop-41 ing high-speed post-processing modules 24 , exploiting high-42 dimensional quantum states 25 , and using heterogeneous mul-43 ticore fiber 26 . The latest SKR performance has reached 10 44 Mbps@10km. For CV-QKD, by controlling the excess noise 45 of the system and increasing the post-processing performance, 46 the SKR has also been significantly improved [27][28][29] . Moreover, 47 due to the encoding scheme, the theoretical SKR generated by 48 CV-QKD in the theoretical asymptotic regime can be close to 49 the ideal SKR performance curve without relay, which scales 50 as 1/2 of the PLOB bound 30 . 51 At present, the SKR of CV-QKD is mainly limited by 52 the system repetition rate. The classical coherent optical 53 communication, which has a similar optical system structure, 54 can reach the repetition rate of even 100 GBaud 31 , whereas 55 Gaussian-modulated CV-QKD has been below 100 MBaud 56 for a long time. The restriction of repetition rate mainly comes 57 from three aspects: 58 1. Signal modulation rate. Gaussian modulation is differ-59 ent from the conventional modulation format, requiring 60 higher modulation accuracy, and otherwise, unacceptable 61 modulation noise will be introduced. In standard Gaus-   It is a straightforward idea to use high-speed classical de-81 vices with well-designed algorithms to solve the above prob-82 lems. However, most quantum information technologies rely 83 on dedicated quantum devices, and the mature classical com-84 ponents have advantages in performance and cost but do not 85 work in the quantum regime. Therefore, using classical com-86 ponents to exhibit quantum effects and further implement 87 quantum information technology is highly challenging, but 88 once it works, its performance can be significantly improved.

89
In this paper, we report a complete CV-QKD system com- terms of components has been broken, which opens the way to 104 establish a high-speed and cost-effective QKD network using 105 mature telecom components directly.

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Protocol and secret key rate 108 CV-QKD with Gaussian modulation can be implemented ac-109 cording to the preparation-and-measurement model, which 110 is schematically depicted in Fig. 1. In this protocol, Alice 111 uses the laser source to prepare the original coherent states. 112 Then these states are modulated following the Gaussian distri-113 bution. That is, Alice first prepare Gaussian random number 114 vector {x a , p a }, and then load it on the origin coherent state to 115 generate the coherent state |x a + ip a . Moreover, she needs to 116 adjust the attenuation to set the desired quadrature component 117 variance value V A of the output coherent states. After being 118 transmitted through the quantum channel, the quantum signal 119 is detected by a homodyne detector or a heterodyne detector. 120 In this work, the heterodyne detector is adopted to achieve 121 phase recovery easily. Specifically, The quantum signal is 122 first divided equally by a 50 : 50 BS and then detected by two 123 homodyne detectors to obtain the quadrature component value 124 of x B and p B , respectively. The theoretical security of GMCS 125 CV-QKD is proved through the entanglement-based model, 126 and the achievable SKR at a specific distance is estimated 127 according to the information theory. In the asymptotic conditions, the achievable SKR generated by CV-QKD can be calculated as where f e is the effective symbol rate, I AB is the classical 129 mutual information between Alice and Bob, χ BE is the Holevo 130 bound on the information leaked to Eve, β is the reconciliation 131 efficiency, FER is the frame error rate of the reconciliation, a 132 is the overhead for frame synchronization, ν is the key fraction 133 disclosed for parameter estimation. The detailed derivation of 134 SKR is given in Supplemental Material.

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In an actual system, the fraction disclosed for parameter es-136 timation ν has an optimal value and can be calculated 33 . The 137 overhead a is determined according to the actual channel con-138 dition. The frame error rate and reconciliation efficiency are 139 related to the selected decoder-the selected decoder should 140 2/11 trade off these two parameters. The amount of mutual information I AB and χ BE are both related to the modulation variance 142 V A , so V A has an optimal value to maximize the difference 143 between the two. χ BE is also related to the critical parameter 144 excess noise ε. The larger ε is, the greater the amount of 145 information leaked to Eve, and even make SKR drop to 0. 146 Therefore, controlling the excess noise is essential. According 147 to the formula, it can intuitively be seen that by increasing the 148 repetition rate, SKR will increase proportionally. However, 149 it is also necessary to ensure the accurate modulation and  Gaussian modulation is a crucial criterion in the theoretical 214 CV-QKD protocol, making it convenient to use Gaussian op-215 timality to realize unconditional security proof. Therefore, 216 to be consistent with the theoretical protocol, the transmitter 217 must also perform the Gaussian modulation format. Specifi-218 cally, the amplitude of the modulated electrical signal at the 219 transmitter is restricted to the linear interval of the response 220 function of the IQ modulator to ensure the Gaussian prop-221 erty of the modulated optical field, and the coherent detection 222 at the receiver is also within the linear operating interval. 223 In Fig. 4, the distribution of the modulation data at Alice 224 and the received data at Bob (after digital signal processing) 225 are shown in (a) and (b), respectively. The Gaussian perfor-226 mance is tested by Shapiro and Wilk's W-test 40 . Results show 227 that at the significance level of α = 0.05, both the modula-228 tion and received data obey the Gaussian distribution (W-test 229 statistic W=0.995, 0.997, P-value=0.182, 0.799), proving the 230 Gaussian performance. Moreover, Fig. 4(c) shows the linear-231 ity of the transmitted data and the received data. The SNR 232 of the quantum signal is 2.58 dB, and the statistical sample 233 size is 10 4 . The slope of the fitting curve is k = 0.996, ex-234 pressing the consistency of data sent and received. Fig. 4(d) 235 is the raw collected data at the receiver, including quantum 236 signal and pilot. The SNR of the pilot is set as 12.53 dB. 237 Due to the phase derivation, the pilot data forms a ring in the 238 phase space, and the signal data maintains a two-dimensional 239 Gaussian distribution. In the experiment, equally spaced pilot signals are inserted 242 between the quantum signals to compensate for the frequency 243 offset and phase drift caused by the independent LO laser. 244 Specifically, we use the same IQ modulator to generate an 245 interleaved pilot signal when preparing a quantum signal. The 246 intensity of the generated pilot signal is entirely proportional 247 to the amplitude of the modulated electrical signal, so it is 248  • t pilot '  In addition, we also analyzed the frequency offset (FO) of 261 the two lasers through the pilot, which is shown in Fig. 5 262 (b). The red color represents the FO of the two NKT narrow-263 linewidth lasers at different times. Due to the high stability 264 of the laser wavelength (±0.04 pm within 60 min), the FO 265 changes very slightly. The FO of the two commercial Inte-266 grable Tunable Laser Assembly (ITLA) lasers represented in 267 blue is used for comparison. Since its stability is only ±1 pm 268 within 15 min, it will jitter at MHz level in a short period and 269 finally exceed the detector bandwidth after a while. There-270 fore, for ITLA lasers, the center wavelength will be controlled 271 through real-time feedback algorithms to ensure long-time 272 system operation in the next step.

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Excess noise measurement 274 In the actual key distribution procedure, a data frame is com-275 posed of the frame header, pilot, and raw key data. The length 276 of one frame is 5 × 10 5 , where the frame header occupies 277 1 × 10 3 , data occupies 2.49 × 10 5 , and the interleaved pilot 278 is 2.5 × 10 5 . After receiving, the signal will be processed 279 through a series of digital signal processing algorithms (in-280 troduced in Methods), and finally, recover the original key 281  and therefore need to be estimated accurately. The traditional 284 parameter estimation scheme is adopted 41 . Fig. 6 shows the 285 excess noise measured by the system under a 20 km standard 286 telecommunication fiber. By testing 20 data frame, the aver-287 age value of the excess noise is 0.062, which can be below 288 the 10 Mbps threshold bound and therefore has 10 Mbps SKR 289 capability. In the experiment, the remaining excess noise of 290 the system mainly comes from the limited phase compensa-291 tion accuracy, while the excess noise fluctuation comes from 292 the device's instability. For example, the jitter of the laser 293 intensity will cause the signal modulation variance and pilot 294 power changes.  Table 1.
Secret key rate analysis 296 According to the measured excess noise and the key exper-297 imental parameters (shown in Table 1, the SKR that can be 298 achieved in the experiment is shown in  five-pointed star is the achieved SKR after post-processing.

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Since the reconciliation efficiency and FER are changed at dif-  It can be seen that our work has apparent advantages within 325 100 km transmission distance compared with previous work.

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In addition, the theoretical SKR of one-way DV-QKD under 327 the same repetition rate is also compared. It can be seen that [46] [35] [43] [44] [42] [36] [17] [45] [47] [13] [14]  considered in this work. It can be mitigated by employing 351 high-speed ADCs to acquire a larger block in the next step. 352 Moreover, with the improved hardware capacity, real-time 353 secret key generation can also be implemented. Our work 354 verifies the feasibility of GMCS CV-QKD with high-speed 355 mature telecom components. The achieved SKR is higher than 356 state-of-the-art GMCS CV-QKD experiments. Considering 357 that existing coherent optical modules such as CFP-ACO 358 are also constructed by these mature components, this work 359 provides a high-speed and cost-effective QKD system scheme 360 to build the future quantum communication network.

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Peak Searching and shot noise calibration 363 Since the oscilloscope that collects the data is triggered by 364 the same clock source as the signal generator for synchronous 365 sampling, we only need to find the peak point for each pulse. 366 Considering that the sampling rate is 10 GS/s and the sym-367 bol rate is 500 MHz, the first 40 sampling data x Bi and p Bi 368 (covering one quantum signal and one pilot signal) is used to 369 calculate the corresponding power, i.e., P i = x 2 Bi + p 2 Bi . Since 370 6/11 the pilot has high power, the index i corresponding to the 371 maximum power value P i is the optimal sampling position.

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Considering that the oversampling ratio is 20, we take this Step 2. Get conversion ratio r = var{x pilot }/var{p pilot }. 401 Step 3. All the p component data p sig , p pilot is scaled by 402 p pilot1 = p pilot × r, p sig1 = p sig × r. After scaling, quadrature 403 component data is balanced.

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Frequency offset estimation 405 After quadrature balance calibration, we need to estimate the 406 frequency offset. The frequency offset comes from the in-407 consistency of the center wavelength of the two lasers. We 408 perform Fourier transform on the pilot signal to find the maxi-409 mum value f o f f , which corresponds to the frequency offset. 410 However, the direction of frequency offset cannot be judged. 411 According to the traditional method in classical optical com-412 munication 50 , the pre-compensation of frequency offset is 413 executed on the pilot signal. We can determine the correct 414 direction according to the variance of the data in both cases. 415 If the compensation direction is wrong, the pilot signal will 416 not converge to a fixed point (see Supplemental Material for 417 more details).

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Phase compensation 419 After the frequency offset is estimated, the phase drift in the 420 quantum signal is compensated. Unlike classical coherent 421 optical communication, the phase deviation due to frequency 422 offset is not compensated in the previous stage but this stage. 423 According to the estimation of frequency offset and the pilot 424 signal, the phase drift is recovered. The phase compensation 425 method is based on 34     The data that support the plots within this paper are available 479 from the corresponding authors on reasonable request.