⇦Chinese Physics Letters, 2022, Vol. 39, No. 7, Article code 070301 Twin-Field Quantum Key Distribution Protocol Based on Wavelength-Division-Multiplexing Technology Yanxin Han (韩雁鑫)1, Zhongqi Sun (孙钟齐)1, Tianqi Dou (窦天琦)2, Jipeng Wang (王吉鹏)1, Zhenhua Li (李振华)1, Yuqing Huang (黄雨晴)1, Pengyun Li (李鹏云)3, and Haiqiang Ma (马海强)1* Affiliations 1School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China 2China Telecom Research Institute, Beijing 102209, China 3China Academy of Electronics and Information Technology, China Electronic Technology Group Corporation, Beijing 100041, China Received 14 April 2022; accepted; published online 17 June 2022 *Corresponding author. Email: hqma@bupt.edu.cn Citation Text: Han Y X, Sun Z Q, Dou T Q et al. 2022 Chin. Phys. Lett. 39 070301    Abstract Quantum key distribution (QKD) generates information-theoretical secret keys between two parties based on the physical laws of quantum mechanics. Following the advancement in quantum communication networks, it becomes feasible and economical to combine QKD with classical optical communication through the same fiber using dense wavelength division multiplexing (DWDM) technology. This study proposes a detailed scheme of TF-QKD protocol with DWDM technology and analyzes its performance, considering the influence of quantum channel number and adjacent quantum crosstalk on the secret key rates. The simulation results show that the scheme further increases the secret key rate of TF-QKD and its variants. Therefore, this scheme provides a method for improving the secret key rate for practical quantum networks.
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 DOI:10.1088/0256-307X/39/7/070301 © 2022 Chinese Physics Society Article Text Quantum key distribution (QKD) provides an information-theoretical secure method for distributing secret keys between distant parties based on the principle of quantum mechanics.[1] The first proposed QKD protocol in 1984[2] has received significant attention.[3–10] However, in applications, concerns with practical devices may result in the use of idealized models without security analysis. The proposed decoy state[11,12] protocol can handle the security issue of photon number splitting (PNS)[13] caused by the imperfect photon source, making QKD useful under weak coherent pulses. In addition, the measurement device-independent QKD (MDI-QKD) protocol was proposed in 2012,[14] having the advantage of immunity against all attacks on the detector side, which further improves the actual security of QKD. QKD has achieved a longer realizable distance[15] and higher secret key rate[16] due to the various theoretical and experimental research on it. However, the maximum possible key rate for communication between users in the absence of quantum memory is limited to the linear key rate Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound, which can be expressed as $R \le -{\log _2}(1-\eta)$, where $\eta$ is the transmittance of the experiment setups.[17] Fortunately, the secret key rate of the twin-filed QKD (TF-QKD) protocol proposed in 2018 is described as $R \sim O(\sqrt \eta)$,[18] which exceeds the PLOB bound. TF-QKD has a higher final key rate than MDI-QKD because it not only retains all the advantages of MD-QKD but is also caused by single-photon interference. Inspired by the original TF-QKD, several theoretical studies and variants[19–21] that further enhance the secret key rate of QKD systems have been proposed. Currently, the application of QKD has been extended from point-to-point communication to optical network communication. Most of the fiber-based QKD experiments use dark fiber as the quantum channel. However, the demand for dark fiber increases as the number of quantum secure communication network users increases, resulting in a sharp rise in deployment costs. Moreover, although the existing key rate has been improved, it cannot satisfy the requirements of the QKD network for information transmission. An effective solution is to carry multiple quantum and classical data signals on a single fiber for simultaneous transmission, and wavelength division multiplexing (WDM)[22] is a standard technique of this scheme. Previous research[23–32] showed that WDM technology combines the existing communication network with the QKD network to send more quantum signals in the same transmission distance, effectively improving the key transmission rate. Further, the combination of mode-pairing MDI-QKD protocol[33] and WDM technology can not only reduce the experimental difficulty but also improve the key rate, providing a new direction for developing QKD networks. However, most of the previous QKD schemes based on WDM technology only considered the effect of classical signals on QKD performance and are yet to consider quantum signals. In this study, we present a detailed scheme for a TF-QKD protocol using dense-WDM (DWDM)[34] technology and analyze its performance. We have used numerical simulations to analyze the feasibility of considering different numbers of quantum channels and the effect of crosstalk on adjacent quantum channels. In addition, we analyze the performance of PM-QKD using the DWDM technology to verify that a TF-QKD variant combined with the DWDM technology has the same performance.
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Fig. 1. (a) Schematic of TF-QKD system based on DWDM. (b) Schematic of Alice and Bob sending pulses. LS: Laser source; Sync: Synchronization clock; VOA: variable optical attenuator; DWDM: dense wavelength division multiplexer; EDFA: erbium-doped fiber amplifier; NBF: narrow-band optical filter; D: single-photon detector; IM: intensity modulator; PM: phase modulator; RNG: random number generator.
Figure 1(a) illustrates the schematic of the TF-QKD system based on DWDM. Figure 1(b) shows that Alice and Bob have the same sending setup in each channel. The goal of Charlie's classical signals is to synchronize Alice's and Bob's signals. For quantum signals, Alice and Bob use the DWDM techniques to combine independent random phase pulses through variable optical attenuators (VOAs) and then send them to Charlie. Charlie uses the DWDM to separate the quantum signals and announce the response of the detector. In this process, a dispersion compensated fiber is selected to minimize the effect of dispersion on the transmitted pulse signal, erbium-doped fiber amplifiers (EDFAs) are used to amplify and recover the Sync signal, and narrow-band optical filters (NBFs) are used to filter out spontaneous Raman noise.[35,36] The protocol's specific process is as follows: In the above process, the phase randomization of the phase slice causes the random phases loaded by Alice and Bob to be different. However, Alice and Bob discard all mismatched values in step 6, and the random phases, ${\rho _a}$ and ${\rho _b}$, loaded by Alice and Bob will always differ by less than ${{2\pi } / M}$ for a pair of twin fields. In the TF-QKD system, the key bits are distilled only from the intensity class ${\mu _{a,b}} \in \big\{ {\frac{u}{2},\frac{v}{2},\frac{w}{2}}\big\}$, with the probabilities ${p_w} = {p_v} \ll {p_u} = 1-{p_w}-{p_v} \le 1$. For the overall gain, ${Q_u}$ is given by[18] $$ {Q_u} = 1-({1-{P_{\rm dc}}}){}^2{e^{-u\widetilde \eta}},~~ \tag {1} $$ with $\tilde \eta = {\eta _{\det }} \times \hat \eta$. Here ${P_{\rm dc}}, {\eta_{\det}}$ and $\hat \eta $ are the dark count, the detection efficiency of Charlie, and the transmission efficiency, respectively. In addition, the gains ${Q_v}$ and ${Q_w}$ are analogous to ${Q_\mu}$ and can be obtained by replacing $u$ with $v$ or $w$. For the error rates, ${E_u}$ is given as follows:[18] $$\begin{align} {E_u} ={}&\Big\{ {{e^{-u\widetilde \eta[{1-({{e_{\rm opt}}+{E_M}})}]}}- {e^{-u\widetilde \eta({{e_{\rm opt}}+{E_M}})}}}\Big\}\\ &\frac{1}{{2{Q_u}}}({1-{P_{\rm dc}}})+\frac{1}{2},~~ \tag {2} \end{align} $$ where ${e_{\rm opt}}$ is the channel optical error rate, and the error rates ${E_v}$ and ${E_w}$ are analogous to ${E_u}$. Further, ${y_1}$ and ${e_1}$ can be estimated using the decoy-state method:[18] $$\begin{align} &y_{1}=\frac{u^{2} Q_{v} e^{v}-u^{2} Q_{w} e^{w}-(v^{2}-w^{2})}{u(u v-u w-v^{2}+w^{2})},~~ \tag {3} \end{align} $$ $$\begin{align} &{e_1}={{({{E_v}{Q_v}{e^v}-{E_w}{Q_w}{e^w}})}/{[{{y_1}({v-w})}]}},~~ \tag {4} \end{align} $$ where[18] $$ {y_0} = {{({v{Q_w}{e^w}-w{Q_v}{e^v}})}/{({v-w})}}.~~ \tag {5} $$ Compared with the efficient BB84,[37] a distance $L$ in TF-QKD can be regarded as the distance of $\frac{L}{{\rm{2}}}$ in QKD, and can be expressed as[18] $$\begin{alignat}{1} R(\mu, L)={}&\frac{1}{2} \frac{1}{M}\Big[R_{\rm Q K D}\Big(\mu, \frac{L}{2}t\Big)\Big]_{\oplus E_{M}} \\ ={}&\frac{1}{2} \frac{1}{M}\{Q_{1}[1-H_{2}(e_{1})]-f Q_{\mu} H_{2}(E_{\mu})\}.~~~~ \tag {6} \end{alignat} $$ The notation $\oplus {E_M}$ represents the intrinsic quantum bit error rate (QBER) of TF-QKD because of the random phase, the coefficient $\frac{1}{M}$ represents the selection from the phase slice. The optimal ${E_M} \simeq 1.275\% $ can be obtained by setting $M = 16$. Here $f$ accounts for the efficiency of error correction, $H_{2}$ is the binary Shannon entropy, and ${Q_1} = {p_{1/\mu }}{y_1}$ is the lower bound for the single-photon gain. The smaller the channel interval, the more the crosstalk photons generated between channels when using WDM technology to improve the secret key rate of information transmission. In a DWDM system, if multiple quantum signals are simultaneously transmitted to the fiber, the channel crosstalk will severely affect the performance of the QKD system, or even prevent the operation of the QKD system completely. In addition, WDM and demultiplexer with high isolation ratio can isolate the carrier and sideband photon interference of classical light to a certain extent.[38] In TF-QKD based on the WDM system, the input excessive noise power at the Charlie receiver, ${P_{\rm Charlie }}$, within the quantum channel bandwidth of wavelength, ${B_{\rm Q}}$, produces excessive noise, ${P_{\rm c}}$, which is given as follows: $$ P_{\rm c}=4 \eta_{\operatorname{{\det}}} \frac{P_{\rm Charlie }}{h v_{_{\scriptstyle \rm Q}} B_{\rm Q}}.~~ \tag {7} $$ Here, ${h}$ is the Planck constant, and ${\upsilon _{\rm Q}}$ is the optical center frequency of the quantum signal. Because both Alice and Bob transmit information to Charlie in the TF-QKD system, the noise induced by Alice's direct transmission of information to Bob is twice as much,[39] thus the coefficient of Eq. (7) is $4$. We classify the noise photons generated by the crosstalk of adjacent quantum channels as part of the background noise (dark count of the detector) to quantify the effect of noise photons on the system performance. Therefore, the overall gain ${Q_{u}(P_{\rm c})}$ for TF-QKD is expressed as follows: $$ Q_{u}(P_{\rm c})=1-[1-(P_{\mathrm{dc}}+P_{\rm c})]^{2} e^{-u \tilde{\eta}}.~~ \tag {8} $$ The gains ${Q_v}$ and ${Q_w}$ are analogous to ${Q_u}$ and can be obtained by replacing $u$ with $v$ or $w$. Similarly, for the error rates, ${E_u}({{P_{\rm c}}})$ is given as follows: $$\begin{align} {E_u}({{P_{\rm c}}})={}&\{{{e^{-u\widetilde \eta [{1-({{e_{\rm opt}}+{E_M}})}]}}- {e^{-u\widetilde \eta ({{e_{\rm opt}} + {E_M}})}}}\}\\ &\frac{1}{{2{Q_u}({{P_{\rm c}}})}}({1-{P_{\rm dc}}-{P_{\rm c}}}) + \frac{1}{2}.~~ \tag {9} \end{align} $$ In addition, the error rates ${E_v}$ and ${E_w}$ are analogous to ${E_u}$. Therefore, in this study the final secret key rate is given as follows: $$\begin{alignat}{1} R(P_{\rm c})={}&\frac{2}{M}\{Q_{1}(P_{\rm c})[1-H_{2}(e_{1})] \\ &-f Q_{\mu}(P_{\rm c})H_{2}[E_{\mu}(P_{\rm c})]+Q_{0}(P_{\rm c})\},~~ \tag {10} \end{alignat} $$ where ${Q_0}$ is the estimated number caused by zero photon pulses (dark and crosstalk counts). As aforementioned, the TF-QKD protocol has many variants. We use the PM-QKD protocol as an example to analyze the performance of TF-QKD protocol variants with DWDM technology. In the PM-QKD protocol, Alice (Bob) randomly prepares weak coherent states $|\sqrt{\mu_{a}} e^{i(\phi_{a}+\pi k_{a})}\rangle_{A}$ ($|\sqrt{\mu_{b}} e^{i(\phi_{b}+\pi k_{b})}\rangle_{B}$), and adds a random phase ${\phi _A}({{\phi _B}})$ to the weak coherent states. Then, Charlie receives and measures them. According to the measurement results announced by Charlie, Alice and Bob can generate raw key bits after postselection of the cases satisfying ${\phi _A} \approx {\phi _B}$. Thus, the structure setting is also the same as that of TF-QKD protocol. In addition, the PM-QKD not only maintains the characteristics of single-photon interference but also ensures security based on entanglement purification, ensuring that the secret key rate beats the linear bound. In PM-QKD, when Alice and Bob select $\frac{\mu }{2}$, the overall gain and QBER, ${Q_\mu}$ and ${E_\mu}$, are given by[19] $$\begin{align} &{Q_\mu} \approx 1-({1-2{P_{\rm dc}}}){e^{-\eta \mu }},~~ \tag {11} \end{align} $$ $$\begin{align} &{E_\mu} \approx ({{P_{\rm dc}}+\eta \mu {e_\delta}})\frac{{{e^{-\eta\mu}}}}{{{Q_\mu}}}.~~ \tag {12} \end{align} $$ Both ${Q_\mu}$ and ${E_\mu}$ can be directly estimated in the experiment. The secret key rate of the PM-QKD protocol can be expressed as[19] $$ R=\frac{2}{M}{Q_\mu}[{1-{f}H_{2}({{E_\mu}})-H_{2}({E_\mu^X})}],~~ \tag {13} $$ where $\frac{2}{M}$ is the sifting factor; ${E_\mu ^X}$ is the phase error rate reflecting the information leakage, which can be bounded by[19] $$ E_\mu ^X \le {\rm{e}}_0^Z{q_0} + \sum\limits_{k = 0}^\infty {{\rm{e}}_{2k + 1}^Z{q_{2k + 1}}}+\Big(1-{q_0}-\sum\limits_{k = 0}^\infty {{q_{2k+1}}}\Big).~~ \tag {14} $$ Here, $q_k$ is the estimated ratio of the “$k$-photon signal” to the full detected signal:[19] $$ {q_k} = \frac{{({{{{e^{-\mu}}{\mu^k}}/{k!}}}){Y_k}}}{{{Q_\mu }}},~~ \tag {15} $$ where ${Y_k}$ and ${e_k^Z}$ are the yield and bit error rate, respectively; when Charlie's light source is a $k$-photon number state, we have[19] $$\begin{align} &{Y_k} \approx 1-({1-2{P_{\rm dc}}}){({1-\eta})^k},~~ \tag {16} \end{align} $$ $$\begin{align} &e_k^Z \approx \frac{{{P_{\rm dc}}{{({1-\eta})}^k}+{e_\delta}[{1-{{({1-\eta})}^k}}]}}{Y_k},~~ \tag {17} \end{align} $$ where ${e_\delta } = \frac{\pi }{M}-\frac{{{M^2}}}{{{\pi ^2}}}{\sin ^3}(\frac{\pi}{M})$ is the misalignment error rate. The PM-QKD system using DWDM is similar to a TF-QKD system. Likewise, when DWDM technology is applied to the PM-QKD, multiple quantum signals are simultaneously transmitted to the fiber and there are crosstalk photons that can affect performance. Therefore, the overall gain and QBER, $Q_{\mu}(P_{\rm c})$ and $E_{\mu}(P_{\rm c})$, are given as follows: $$\begin{align} &Q_{\mu}(P_{\rm c})\approx 1-[1-2(P_{d c}+P_{\rm c})] e^{-\eta \mu},~~ \tag {18} \end{align} $$ $$\begin{align} &E_{\mu}(P_{\rm c})\approx(P_{d c}+P_{\rm c}+\eta \mu e_{\delta})\frac{e^{-\eta \mu}}{Q_{\mu}(P_{\rm c})}.~~ \tag {19} \end{align} $$ In addition, $$\begin{alignat}{1} &Y_{k}(P_{\rm c}) \approx 1-[1-2(P_{d c}+P_{\rm c})](1-\eta)^{k},~~ \tag {20} \end{alignat} $$ $$\begin{alignat}{1} &q_{k}(P_{\rm c})=\frac{(e^{-\mu} \mu^{k}/k!) Y_{k}(P_{\rm c})}{Q_{\mu}(P_{\rm c})},~~ \tag {21} \end{alignat} $$ $$\begin{alignat}{1} &e_{k}^{Z}(P_{\rm c})\approx \frac{(P_{d c}+P_{\rm c})(1-\eta)^{k}+e_{\delta}[1-(1-\eta)^{k}]}{Y_{k}(P_{\rm c})}.~~~~~~~ \tag {22} \end{alignat} $$ Thus, ${E_{\mu}^{X}(P_{\rm c})}$ are also affected by crosstalk photons. The final secret key rate is given by $$\begin{align} R(P_{\rm c})={}&\frac{2}{M}\{Q_{\mu}(P_{\rm c}){[1-{f} H_{2}[E_{\mu}(P_{\rm c})]-H_{2}[E_{\mu}^{X}(P_{\rm c})]]} \\ &+Q_{0}(P_{\rm c})\} .~~ \tag {23} \end{align} $$ We used numerical simulations to analyze the performance of TF-QKD based on the DWDM technology. First, we discuss the effect of the number of quantum channels on the key rate. Then, we simulate the secret key rate of TF-QKD, and Table 1 lists the values of parameters. Figure 2 shows the simulation results of the secret key rate in TF-QKD with the different numbers of WDM channels. The results show that the secret key rate of TF-QKD with the multichannel simultaneous transmission is higher than the single-channel transmission under the same distance, and the trend of increasing security key rate is not linear.
Table 1. Values of parameters in simulation.
Parameters $M$ $f$ $u$ $v$ $w$ ${e_{\rm opt}}$ ${\eta _{\det}}$ ${P_{\rm dc}}$ (per pulse)
Values 16 1.15 0.4 ${10^{-2}}$ ${10^{-4}}$ 3% 30% ${1 \times {10^{-8}}}$
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Fig. 2. Secret key rate of TF-QKD based on DWDM. The lines from top to bottom are the secret key rates for different numbers ($N=40,\, 20$, and 1).
The numerical simulation parameters for the PM-QKD protocol are listed in Table 2, and the result of the numerical simulation is shown in Fig. 3. Compared with the application without DWDM technology, the secret key rate of PM-QKD based on DWDM is higher and increases as the number of channels increases, like the purple and green lines. Because the TF-QKD variants are derived from the original TF-QKD, DWDM technology can be applied to the TF-QKD and to its variants by simultaneously transmitting multiple wavelengths carrying information.
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Fig. 3. Secret key rate of PM-QKD based on DWDM. The lines from top to bottom are the secret key rates for different numbers ($N=40,\, 20$, and 1).
Table 2. Values of parameters in simulation of PM-QKD.
Parameters $M$ $f$ ${\mu}$ ${\eta_{\det}}$ ${P_{\rm dc}}$ (per pulse) ${e_\delta}$
Values 16 1.15 0.3 14.5% ${8 \times {10^{-8}}}$ 1.5%
Then, we discuss the effect of quantum channel noise-induced crosstalk on the secret key rate. As an example, we compare and analyze the secret key rate of a single channel with and without DWDM at 1550 nm wavelength. Figures 4 and 5 show the simulation results of the key rate of TF-QKD and PM-QKD with different crosstalk photons. The key rate and transmission distance of TF-QKD and PM-QKD decrease as the DWDM crosstalk noise increase. We will use TF-QKD as an example (Fig. 4). The blue line represents the secret key rate without the DWDM technology. The red line represents the secret key rate with crosstalk only affected by one channel, and the value of $P_{\rm c}$ is the same as the value of the detector's dark count, corresponding to the first and last channels. The yellow line represents the secret key rate with crosstalk affected by two channels, corresponding to the middle channels, with the value of $P_{\rm c}$ equal to two times the dark count. If the quantum signal is multiplexed with the classical signal, the crosstalk between the channels will increase significantly and the corresponding secret key generation rate will drop rapidly, as depicted by the purple line. However, the total secret key rate increases for all channels. The analysis and results for PM-QKD are the same for TF-QKD (Fig. 5). Therefore, the TF-QKD and its variants based on DWDM technology can simultaneously send information from multiple wavelengths and increase the total secret key rate, providing a solution to satisfy the requirements of future large-scale networks.
cpl-39-7-070301-fig4.png
Fig. 4. Secret key rate of TF-QKD for a single channel at different crosstalk photon counts. The lines from left to right are the secret key rate for different numbers of crosstalk photons ($P_{\rm c} = 10\times 10^{-8}$, $2\times 10^{-8}$, $1\times 10^{-8}$ and 0).
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Fig. 5. Secret key rate of PM-QKD for a single channel at different crosstalk photon counts. The lines from left to right are the secret key rate for different numbers of crosstalk photons ($P_{\rm c} = 10\times 10^{-7}$, $2\times 10^{-7}$, $1\times 10^{-7}$ and 0).
In summary, we have proposed a detailed scheme of TF-QKD protocol based on DWDM technology and analyze its performance, transmitting multiple pulse signals using the same fiber. In our analysis, we consider two main factors affecting the performance: the number of quantum channels and the crosstalk photons between adjacent quantum channels. The simulation results show that the overall secret key rate of the TF-QKD system can be significantly improved, though the key rate per channel is reduced. The behavior of this system can be effectively improved by increasing the number of quantum channels and reducing the crosstalk of adjacent quantum channels. Moreover, we use the PM-QKD protocol as an example to ensure that the variant form of the TF-QKD protocol combined with DWDM has the same characteristics. Notably, we propose a method to increase the key rate, which provides a reference for realizing multiuser quantum communication in the future. Acknowledgment. This work was supported by the State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications (Grant No. IPOC2021ZT10), the National Natural Science Foundation of China (Grant No. 11904333), the Fundamental Research Funds for the Central Universities (Grant No. 2019XD-A02), and BUPT Innovation and Entrepreneurship Support Program (Grant No. 2022-YC-T051). References Quantum cryptography: Public key distribution and coin tossingMixed-state entanglement and quantum error correctionPractical challenges in quantum key distributionFocus on Quantum Cryptography: Theory and PracticeA Fully Symmetrical Quantum Key Distribution System Capable of Preparing and Measuring Quantum StatesContinuous-Variable Measurement-Device-Independent Quantum Key Distribution with One-Time Shot-Noise Unit CalibrationQuantum cryptographyProof of Security of a Semi-Device-Independent Quantum Key Distribution ProtocolExperimental Point-to-Multipoint Plug-and-Play Measurement-Device-Independent Quantum Key Distribution NetworkDecoy-state protocol for quantum cryptography with four different intensities of coherent lightDecoy State Quantum Key DistributionLimitations on Practical Quantum CryptographyMeasurement-Device-Independent Quantum Key DistributionSecure Quantum Key Distribution over 421 km of Optical FiberFundamental rate-loss tradeoff for optical quantum key distributionFundamental limits of repeaterless quantum communicationsOvercoming the rate–distance limit of quantum key distribution without quantum repeatersPhase-Matching Quantum Key DistributionTwin-field quantum key distribution with large misalignment errorTwin-Field Quantum Key Distribution without Phase PostselectionReview and status of wavelength-division-multiplexing technology and its applicationSimultaneous quantum cryptographic key distribution and conventional data transmission over installed fibre using wavelength-division multiplexingExperimental characterization of the separation between wavelength-multiplexed quantum and classical communication channelsQuantum key distribution for 10 Gb/s dense wavelength division multiplexing networksExperimental integration of quantum key distribution and gigabit-capable passive optical networkWavelength division multiplexing of continuous variable quantum key distribution and 18.3 Tbit/s data channelsIntercore spontaneous Raman scattering impact on quantum key distribution in multicore fiberModeling and Minimizing Spontaneous Raman Scattering for QKD Secured DWDM NetworksFinite-key analysis based on neural network of practical wavelength division multiplexed decoy-state quantum key distributionMeasurement-Device-Independent Quantum Key Distribution of Frequency-Nondegenerate Photons10-Gb/s data transmission using optical physical layer encryption and quantum key distributionQuantum key distribution surpassing the repeaterless rate-transmittance bound without global phase lockingQuantum key distribution for 10 Gb/s dense wavelength division multiplexing networksCoexistence of High-Bit-Rate Quantum Key Distribution and Data on Optical FiberDense wavelength multiplexing of 1550 nm QKD with strong classical channels in reconfigurable networking environmentsEfficient Quantum Key Distribution Scheme and a Proof of Its Unconditional SecurityHigh-speed wavelength-division multiplexing quantum key distribution systemReference-frame-independent quantum key distribution of wavelength division multiplexing with multiple quantum channels*
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