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Abstract
We present a versatile transmitter capable of performing both discrete variable and continuous variable quantum key distribution protocols (DV-QKD and CV-QKD, respectively). Using this transmitter, we implement a time-bin encoded BB84 DV-QKD protocol over a physical quantum channel of 47 km and a GG02 CV-QKD protocol with true local oscillator over a 10.5 km channel, achieving secret key rates of 4.1 kbps and 1 Mbps for DV- and CV-QKD, respectively. The reported transmitter scheme is particularly suitable for re-configurable optical networks where the QKD protocol is selected to optimize the performance according to the parameters of the links.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum key distribution (QKD) is a technology that allows exchanging highly secure cryptography keys between two remote parties [1,2]. The security of QKD relies on the laws of quantum mechanics, which allows revealing the presence of an eavesdropper in the communication channel. QKD combined with one-time-pad (OTP) can provide information-theoretic security [3].
QKD can be divided into two main categories: Discrete Variable (DV) and Continuous Variable (CV) [4]. In DV-QKD, considering prepare-and-measure settings, the emitter (Alice) prepares and sends to a receiver (Bob) quantum signals, which consist of single photons with encoded random data. The encoding is done following a specific QKD protocol by using a discrete-valued degree of freedom of the photons such as polarization [5], time-bin [6] or linear momentum [7]. Bob measures the state of the arriving photons by relying on single-photon detection, and obtains data that are partially correlated to the data encoded by Alice. These data can be used to distill a secret key by means of error correction and privacy amplification [3]. In CV-QKD, the quantum signals typically consist of coherent states of light with information encoded in the quadratures of electromagnetic fields [8]. Instead of single photon detectors, CV-QKD uses coherent homodyne or heterodyne detection (known in telecommunication phase-diversity homodyne detection) to retrieve the quadratures value of the signal and thus distill a secret key [8–11]. Significant effort has been made on the integration of QKD into optical networks, aiming at protecting digital data in the near future, as expected advances in quantum computers could make vulnerable some of the most widely used cryptography methods, such as Rivest-Shamir-Adelman (RSA) and Diffie-Hellmam [12].
DV- and CV-QKD have both been demonstrated in network configurations [13–15]. For example, the QKD network SECOQC, which was based on DV-QKD hardware, had also a CV-QKD link [15].
A performance comparison in terms of secret key rate between DV- and CV-QKD would largely depend on the electronic and optical components used to build the systems. Nevertheless, there are some intrinsic characteristics of DV- and CV-QKD that could influence the choice between the two technologies to be used in a network. For instance, DV-QKD is in general more tolerant to channel losses. In CV-QKD, the signal-to-noise ratio rapidly decreases with channel losses, as data to generate the key are obtained for each transmitted quantum signal. Contrarily, in DV-QKD, the key is made of data obtained only from the received quantum signals. Hence, fiber demonstrations of DV-QKD have been possible over distances larger than those of CV-QKD, e.g. 421 km [16] compared to 202.81 km for CV-QKD [17]. Nevertheless, at short distances, CV-QKD could in principle allow for a key rate higher than DV-QKD as more than one secret bit per symbol could be extracted [18], and coherent detectors do not suffer from dead time present in single-photon detectors [19]. In addition, CV-QKD can be readily used in coexistence with classical communication in the same fiber by means of wavelength-division multiplexing [20,21]. The coherent detection used in CV-QKD acts as a filter to light at wavelength different from that of the local oscillator [22]. Recently, CV-QKD coexistence with 18.3 Tb/s data channel in the C-band was demonstrated over a fiber channel of 10 km [23]. In terms of cost, CV-QKD hardware could have a price significantly lower than the one of DV-QKD, especially because CV-QKD does not need single-photon detectors. A comparative summary of the different implementations of DV- and CV-QKD in terms of secret key rate and distance can be found in Ref. [24], and in terms of coexistence capabilities in Ref. [23].
In a network environment, considering the advantages of each scheme, the choice between DV- or CV-QKD would depend on the fiber link characteristics such as losses or power and number of co-propagating classical data channels. Modern re-configurable and software defined networks [25] could allow for selecting between DV- and CV-QKD technology, if both systems are present in the nodes of a network, in order to maximize the QKD performance for a given link between two different nodes. Moreover, one can envisage a network where versatile transmitters and receivers capable of performing DV- and CV-QKD are placed at the nodes, and the selection is dynamically performed by the network controller.
Here we propose a single transmitter capable of generating quantum signals for both DV- and CV-QKD protocols using the underlying software configuration. To demonstrate the proposed transmitter, we carry out DV- and CV-QKD experiments over a fiber link of 47 and 10.5 km, respectively. For DV-QKD, we implement a decoy-state BB84 protocol [1,26] with time-bin encoding, and for CV-QKD we use a Gaussian-modulation protocol with true local oscillator [20,27]. An asymptotic secret key rate of 4.1 kbps and 1.06 Mbps are obtained for DV- and CV-QKD, respectively.
We note that versatile multi-protocol transmitters have been demonstrated by using dual drive phase modulators [28] and phase controlled injection-locking [29]. These transmitters could in principle prepare quantum signals for all QKD protocols based on coherent states with phase and amplitude modulation. Nevertheless the practical demonstrations of these transmitters have been limited only to DV-QKD protocols, such as coherent one way (COW) and differential phase shift (DPS). Here we extend the previous work by proposing and demonstrating a transmitter capable of preparing quantum signals for CV- and DV-QKD protocols. The capability of switching between CV- and DV- protocol by using a single transmitter could facilitate the integration of QKD in a network environment by selecting the protocol according to the link, in this way facilitating the wide-scale deployment of QKD and allowing distribution of keys between cities as well as in metropolitan networks. In addition, the presented transmitter could find application in the context of agile and versatile quantum cryptography, where the same hardware could allow for several cryptography tasks [30].
2. Experimental setup
Figure 1 shows the experimental scheme of the proposed transmitter. The light source is a continuous wave tuneable (CW) external cavity laser (ECL) emitting at 1550 nm with a line-width of 10 kHz. Three amplitude modulators AM1, AM2 and AM3 (IMP-1550-10-PM-HER, Optilab) and one phase modulator PM (MPZ-LN-01, iXblue) are used to create optical pulses with the modulation required by each QKD protocol. Subsequently, an electrically-controlled variable attenuator (VOA1) is used to set the mean photon number per symbol at Alice’s output. A field programmable gate array (FPGA, Xilinx ZC706) combined with a 16-bit two output digital-to-analog converter (FMCDAQ2, Analog devices) generates patterns of electrical signals to drive the electro-optic modulators and the VOA1. The FPGA also sends a clock signal that is used to synchronize the emitter and receiver stations for the DV-QKD implementation. A 99/1 beam splitter (BS3) is used to send $99\%$ of the light to a power meter (PoM) to calibrate the mean photon number per symbol. The remaining $1\%$ continues to Alice’s output where an optical isolator is placed to prevent Trojan horse attacks [31].
Fig. 1. Scheme of the proposed transmitter (ALICE-DVCV). A DV- and CV-QKD receiver are connected by a fiber of 47 km and 10.5 km respectively. AM1, AM2 and AM3 are amplitude modulators, PM is a phase modulator, BS are beam-splitters, VOA are variable optical attenuators, ISO is an optical isolator, PoM is a power meter, GC is a HCN Gass Cell, BD is a balanced detector, SW is an optical switch
To stabilize the frequency of the laser, a beam splitter (BS1) is placed before the modulators to separate 10$\%$ of the light, which is then split in two equal parts by a second beam splitter (BS2). One of the outputs of BS2 goes to a fiber-coupled HCN gas cell (GC, Wavelength References HCN-13-25), which is used as frequency reference [32]. The other output of BS2 goes to a variable optical attenuator (VOA2). The output of the GC and the VOA2 are detected by a Balanced Detector (BD). The VOA2 is employed to compensate for the absorption and loss of GC and thus improving the detection sensitivity. The frequency of the laser can be controlled by applying a voltage to a piezoelectric element present in the laser cavity. The laser frequency is locked to an edge of a HCN absorption peak by means of a feedback algorithm implemented on the FPGA. In this demonstration, the center frequency of the laser was set to 193.735 THz (1547 nm) with a standard deviation below 3 MHz. The gas cell was not stabilized in temperature. In the future, temperature stabilization can be considered for stable locking over longer time. We note that commercially-available lasers that are frequency-locked using a HCN gas cell have been previously used in CV-QKD experiments [27,33], representing a practical solution for stabilizing the frequency of the lasers. Finally, an optical switch (SW) is used to send the quantum signals through the fiber link connecting Alice with either DV-QKD or CV-QKD receiver.
2.1 DV-QKD protocol implementation
As mentioned above, we implement a decoy-state BB84 DV-QKD protocol with time-bin encoding (Fig. 2(A)), the transmitted optical symbols are composed of quantum signals used to encode the secret key, decoy-state signals used to characterize the transmission of the quantum channel, and reference signals used to stabilize the detection system. The quantum signals are formed by two coherent light pulses (or time-bins) typically called "early" $\vert {e}\rangle$ and "late" $\vert {\ell }\rangle$ [34,35]:
Fig. 2. A) Optical pulse distribution over time for three types of transmitted signals for DV-QKD implementation (quantum signal, decoy states and reference patterns). The separation between signals is $\Delta t= 50 \textrm {ns}$ and the separation between temporal modes is set to $\delta t = 10 \textrm {ns}$. B) Intensity and phase scheme of the time-bin states required for the BB84 protocol with two decoy states. The mean photon number of the quantum signal and decoys are $\mu$, $\nu _1$ and $\nu _2$ respectively. C) Intensity and phase scheme for the reference pattern used to calibrate the receiver interferometer, the mean photon number for the reference pattern is labeled as $\rho _{\textrm {ref}}$.
Quantum signals are prepared by selecting states from two mutually unbiased bases (Z and X). The Z-basis is composed by two states with single temporal modes, $\ \vert {e}\rangle$ and $\vert {\ell }\rangle$. The X-basis consists of two states that combine the early and late temporal modes with a relative phase equal to $0$ or $\pi$ ($\vert {d_0}\rangle =\vert {\sqrt {\mu /2}}\rangle _e \vert {\sqrt {\mu /2}}\rangle _{\ell },\vert {d_{\pi }}\rangle =\vert {\sqrt {\mu /2}}\rangle _e\vert {e^{i\pi }\sqrt {\mu /2}}\rangle _\ell$). The four time-bin states are shown in Fig. 2(B).
Decoy-states are interleaved among the quantum signals. The symbols encoded by the decoy states are selected among the four states from the X and Z bases, Fig. 2(B). In our implementation, we use two decoy states with mean photon number $\nu _1$ and $\nu _2$ following the relation:
The optimal value of $\mu$, $\nu _1$ and $\nu _2$ is determined by maximizing the possible secret key rate (SKR) [26].
The reference signals are composed by two pulses with a phase difference of $\phi =0$, Fig. 2(C). The mean photon number of the reference pulses is two times that of the quantum signals ($\rho _{\textrm {ref}}\sim 2 \mu$).
In the demonstration presented here, Alice repeatedly sends a fixed pattern consisting of 16 symbols required for the 2-decoy BB84 protocol with interleaved reference patterns. This allows estimating the experimental parameters and characterizing QKD performance. We remark that to distill a secret key in a QKD session, the quantum signals and the decoys should be selected randomly by using for instance a quantum random number generator [36].
To carry out the experimental demonstration of DV-QKD, the electro-optic modulators AM2 and AM3 (Fig. 1) are used to generate the $\vert {e}\rangle$ and $\vert {\ell }\rangle$ modes and thus are driven by identical electrical signals. In our implementation, the width of each pulse forming the quantum signal is 2 ns and the separation between the pulses $\delta t$ is 10 ns. The modulator AM1 is driven by the 16-bit DAC and is used to set the relative mean photon number between the transmitted symbols. Finally, the PM, also controlled by a 16-bit DAC, is used to add a $\pi$ phase difference needed for the X-basis states. We note that the the security proof for the protocol requires phase randomization between symbols. This could be achieved by using the modulator PM to add a random phase to the quantum signals.
The receiver setup for the DV-QKD implementation is shown in Fig. 3(A). An asymmetrical Faraday-Michelson interferometer (AFMI) is used to achieve interferometric visibility without the need of performing active stabilization of polarization. The unbalance between arms is set to match the temporal mode separation $\delta t = 10\ \textrm {ns}$. An InGaAs/InP Single Photon Detector (SPD, IDQ ID210) is placed at the outputs of the AFMI to detect the arrival time of the transmitted symbols and retrieve the four projections from the X and Z bases of the time-bin states [37]. The AFMI is thermally and mechanically isolated. The residual slow thermal drift is compensated by driving a piezo stretcher (FS) placed in one arm of the AFMI in order to minimize the detected counts associated to the reference signal at one output of the interferometer [38]. In the experiment presented here, we use a single SPD detecting one of the outputs of the AFMI at a time, which allows for estimating the parameters of the QKD. However, in a complete QKD session, SPDs would be placed simultaneously at each output of the AFMI [39]. Finally, a time-tagger and a interferometer stabilization algorithm are performed by using an FPGA placed at Bob. The losses at the receiver are 3.7 dB and the SPD quantum efficiency is 10 $\%$.
Fig. 3. A) DV-QKD receiver; AFMI is an asymmetrical Faraday Michelson Interferometer, Circ is a circulator, FM is a Faraday mirror, FS is a piezo fiber stretcher driven by a High Voltage Driver unit (HVD), SPD is a single-photon detector. The curves next to the AFMI outputs (A and B) represent the probability distribution of the $\vert {d_0}\rangle$ state. An FPGA controls the interferometer phase stability and includes a time-tag firmware that is used to store the generated raw key. B) CV-QKD receiver; OH is an $90^{\circ }$ optical hybrid, LO is the local oscillator laser, BD is a balanced detector, OSC is an oscilloscope with a sampling of 1GSps and bandwidth limited to 200 MHz. PC is an electrically-driven polarization controller, and SW is an optical switch used to calibrate the shot noise.
2.2 CV-QKD protocol implementation
CV-QKD is performed using a Gaussian-modulated coherent state (GMCS) protocol. In this protocol, Alice encodes the information to generate the key in coherent states (weak laser pulses) with electromagnetic field quadratures (X and P) modulated according to two independent, random, and zero-centered Gaussian distributions [8,40].
The detection of the quantum signals performed by Bob is based on coherent heterodyne detection where X and P quadratures are measured simultaneously [11,41]. The local oscillator required for coherent detection is generated at Bob with an additional laser (i.e. true local oscillator), which avoids calibration attacks [42].
In our implementation, Alice uses an amplitude modulator (AM1) to generate a train of 4 ns full width half maximum (FWHM) pulses from the CW laser source. The repetition rate of the pulses is 31.25 MHz. As depicted in Fig. 4, the train of pulses consists of quantum signal and reference pulses that are interleaved. The reference pulses are used to recover the encoded phase information of the quantum signals by allowing the estimation of the phase difference between laser source and local oscillator, as well as phase fluctuations due to the channel. A description of the phase recovery procedure can be found in [20].
Fig. 4. Optical pulse distribution over time for the CV-QKD implementation (quantum signal, reference pulses). Each pulse presents a FWHM of 4 ns and separation between pulses is $\Delta t = 32$ ns. The reference pulses are interleaved between the quantum signals to allow for phase recovery.
Gaussian distributed quadratures are obtained by modulating the amplitude and phase of the quantum signal according to a Rayleigh random distribution and uniform random distribution respectively [43]. This is carried out by using the amplitude modulator AM1 and the phase modulator PM. The random distributions corresponds to two independent sequences of 4096 pseudo-random numbers. The amplitude and phase of the reference pulses are not modulated. A second amplitude modulator (AM2) is used to increase the extinction ratio of the pulses and minimize the background light. The electrical signal for AM2 consists of 4 ns FWHM pulses with constant amplitude that are aligned to the pulses generated by AM1.
To minimize the noise of the reference pulses and accurately recover the phase information of the quantum signals, the amplitude of the reference pulses is typically much higher than the quantum signal (i.e 500 times in Ref. [44]). The ratio between the amplitude of the reference and signal pulses, R, is controlled by adjusting the bias set-point of the third amplitude modulator (AM3) that operates at half the clock frequency (15.625 MHz). Finally, a VOA, a 99/1 BS, and a PoM are used to set Alice modulation variance $V_{\textrm {mod}}$ in order to maximize the secret key rate. The modulation variance is equal to twice the mean photon number ($V_{\textrm {mod}}=2\langle n\rangle$). We note that, similarly to DV-QKD, using fixed random sequences to generate the signals allows characterizing experimental parameters of the QKD. However, for distilling a secret key in a real application, a continuous source of true random numbers obtained from a quantum random number generator should be used.
The CV-QKD receiver, Fig. 3(B), is composed by an electrically-driven polarization controller (PC) which is used to align the polarization of the received optical signal and the local oscillator. The local oscillator is a 10 kHz line-width ECL laser with a power of 48mW. The signal and the local oscillator laser are interfered by using a $90^{\circ }$ Optical Hybrid ($90^{\circ }$OH), whose four outputs are measured by two BDs. The BDs provide measurements of X and P quadratures, which are digitized using a 1 GSps oscilloscope. An optical switch (SW) is used to block the incoming light from Alice in order to calibrate the shot noise variance, which is used to normalize the quadrature values. The electronic noise variance is calibrated by switching off the local oscillator [20,40]. A 200 MHz low pass filter is used at the input of the oscilloscope to increase the signal to noise ratio, which results in a clearance between the shot noise and electronic noise of 16.7 dB.
3. Experimental results
The adaptable transmitter was demonstrated using two different quantum channels for DV- and CV-QKD with the corresponding receiver, as shown in Fig. 1.
3.1 DV-QKD results
In DV-QKD, the quantum channel is over a 47 km fiber spool (Corning SMF28 ULL fiber) with 8.2 dB total attenuation. For a two-mode time-bin state, each output of the AMZI generates three temporal modes, as shown in Fig. 3(A). The quantum bit error rate (QBER) for each state is calculated as the ratio between the number of wrong detections and the total number of detections [2]:
The total QBER is obtained from the average of the QBER for each state. An early and late state of the Z basis are correctly measured when photons are detected in the first and third temporal mode respectively. In this case, the output A and B of the AFMI have the same detection probability distribution. The $\vert {d_0}\rangle$ and $\vert {d_\pi }\rangle$ states from the X basis are correctly decoded when photons are detected in the second temporal mode the output A and B of the interferometer, respectively.
Alternatively, the QBER could be obtained using only one detector at the output A or B of the AFMI. To this end, the total number of detections for the X basis is estimated using the counts in the first and third temporal modes. This procedure is described in Ref. [37]. For instance, $N_{right}$ and $N_{wrong}$ for the states $\vert {d_0}\rangle$ and $\vert {d_\pi }\rangle$ are obtained from the counts at the output A, $N_A$, as:
To obtain the average QBER, a 150 seconds measurement is performed at the output A and B of the AFMI. Using Eq. (3) and the combined detections at output A and B of the AFMI, a QBER of 1.5$\%$ $\pm$ 0.1$\%$ is obtained for the signal states. We selected a mean photon number for quantum signals of 0.57 $\pm$ 0.01 corresponding to the optimal value considering the characteristics of the quantum channel [26]. The mean photon value for the decoy 1 and 2 states are set to 0.056 $\pm$ 0.002 and 0.014 $\pm$ 0.002, respectively. Subsequently, we study the variation of the QBER and mean photon number as function of time, Figs. 5(A) and 5(B). To this end, the QBER is directly calculated from the 150 seconds measurement at the output A of the AFMI by using Eq. (4). In this case, the mean value for the QBER for the quantum signal and the two decoy states are 1.4 $\pm$ 0.1$\%$, 12.9 $\pm$ 0.9$\%$, and 46 $\pm$ 2$\%$, respectively. The QBER of quantum signals presents similar contributions from the intrinsic QBER and errors related to dark counts of the SPD using 5 ns detection windows per time-bin. The intrinsic QBER for the Z-basis states is 0.3 $\%$, due to the finite extinction of the modulation, while that of the X-basis states is 1$\%$, due to limited interferometric visibility and stabilization of the AFMI.
Fig. 5. Results for the test of the DV-QKD protocol. A) and B) shows the mean QBER and mean photon number obtained for the signal and decoy states using a quantum channel of 47km. C) Estimated secret key Rate for both implementations at 47 and 65.7 km. The solid line represents the estimated SKR as a function of propagation distance, achieving a maximum distance of 70 km for the experimental conditions present in both tests.
A lower bound for the secret key rate per second in the asymptotic limit for the BB84 protocol can be estimated by:
The factor $\frac {1}{2}$ represents the bases coincidence probability, $r_{rate}$ is the repetition rate of the system, $Q_{\mu }$ is the gain of the quantum signal states, $E_{\mu }$ is the mean QBER for the quantum signals, $Q_1^{L,\nu _1,\nu _2}$ is the lower bound for the single photon gain (estimated using the decoy signal yields), $H_2(p)$ is the Shannon binary entropy function, $e_1^{U,\nu _1,\nu _2}$ is the upper bound for the QBER of single photon quantum signals, $f(x)$ is the error correction efficiency. A detailed procedure of the secret key lower bound for the BB84 protocol with 2-decoy states can be found in [26]. Considering the calculated QBER and experimental parameters, a SKR of 4.1 kbps is estimated from the recorded data shown in Figs. 5(A) and 5(B). We note that the SKR estimated by Eq. (5) considers single photon detectors placed simultaneously at both output of the AFMI.
Finally, to characterize the maximum achievable distance of the communicating channel, we increased the fiber length to 65.7 km resulting in 11.4 dB of propagation loss. In this setting, the average QBER is 2.0$\pm$0.3$\%$ and the SKR is 227 bps. We simulated the expected SKR in terms of fiber length obtaining a maximum achievable distance of 70 km, Fig. 5(C).
3.2 CV-QKD results
For CV-QKD, the quantum channel is a 10.5 km (Corning SMF28 ULL fiber) fiber spool with 1.9 dB total attenuation. The correlation between Alice data $q_A=\{X_{Ai},P_{Ai}\}$ and Bob data $q_{B}=\{X_{Bi},P_{Bi}\}$ is limited by the shot-noise and the excess noise $\varepsilon$. The excess noise at the channel output can be estimated by [20,40]:
where $V_{B|A}$ is the conditional variance given by [40]The quantity $\nu _{\textrm {elec}}$ is the electronic noise and $\eta$ is the detection efficiency. In the realistic scenario, $\nu _{\textrm {elec}}$ and $\eta$ are considered trusted and measured before the communication. Therefore $\nu _{\textrm {elec}}$ is subtracted from the total excess noise. The transmittance of the channel $T$ is calculated from the correlation [40]
As mentioned above, $V_{\textrm {mod}}$ is the Alice modulation variance, which is set before the communication. The secret key rate per transmitted symbol $r$ considering the asymptotic limit and reverse reconciliation can be calculated as
$f$ is the reconciliation efficiency, $I_{AB}$ is the mutual information between Alice and Bob, and $\chi _{BE}$ is the Holevo bound. $I_{AB}$ and $\chi _{BE}$ are calculated from the experimental parameters, specifically excess noise, channel transmittance, Alice modulation variance, and detection efficiency. The SKR in bits per second is obtained by multiplying $r$ by the repetition rate of the quantum signal. A detailed description of the calculation of the secret key rate can be found in Ref. [33,40].Experimental results are shown in Fig. 6. Alice modulation variance is set to $V_{\textrm {mod}}=2 \ \textrm {snu}$. The detection noise is $\nu _{\textrm {elec}}=0.021 \ \textrm {snu}$. A reconciliation efficiency $\beta =0.95$ is considered [10]. The detection efficiency is $\eta =0.39$. The ratio between reference pulses and quantum signal is $R=541$. Figure 6(A) shows 16 consecutive measurements taken over 60 minutes of the excess noise (top), the transmittance (middle), and the SKR (bottom). Each point corresponds to blocks of 0.65 x $10^{6}$ symbols. The block length is limited by the memory of the oscilloscope. The excess noise, transmittance and key rate are calculated for each block independently. We note that the 1 GSps oscilloscope could be replaced by a commercial ADC unit with larger memory, which could also allow for continuous streaming and real-time digital signal processing. The shot-noise variance is estimated before each measurement. The excess noise, estimated by using Eq. (6), has a mean value of $0.022 \ \textrm {snu}$ and remains below threshold for null secret key, which is $0.045 \ \textrm {snu}$. The excess noise includes phase estimation error due to time-delay between reference and signal pulses, as well as the noise on reference pulses. The transmittance T, obtained from Eq. (8), has a mean value of 0.64. The value T is stable over the measurement time with a relative standard deviation $2.5 \%$, which means that variations of $V_{\textrm {mod}}$ due to changes in bias-set point of the modulators, as well as changes in polarization are not significant. We note that in a field demonstration with deployed fiber, the received polarization state is expected to change over time, and therefore active compensation would be needed. The SKR is calculated considering the values obtained for $\epsilon$ and $T$ by using Eq. (9). A mean SKR of 1.06 Mb/s is obtained, and it fluctuates between $0.7$ Mb/s and $1.5$ Mb/s during the measurement time. Figure 6(B) shows a simulation of the secret key as a function of transmission distance. It can be seen that, for the experimental parameters calculated above, a positive SKR could be obtained at a distance up to 24 km. This simulation assumes that the excess noise is kept constant at longer distances, which could be achieved by increasing the amplitude of the reference pulses to compensate for the extra loss.
Fig. 6. A) CV-QKD experimental results; 16 measurements of $\approx 0.65$ million samples each were obtained during 60 minutes. Excess noise (top), transmittance (middle) and secret key rate, SKR (bottom). B) Simulation of the SKR as a function of distance
4. Conclusion
The presented experiments demonstrate the use of a single transmitter with switching possibility for CV-QKD and DV-QKD. BB84 DV- and a GG02 CV-QKD were the protocols used in combination with two independent receivers. The DV- and CV-QKD communication channels run over a fiber link with a length of 47 km and 10.5 km, respectively. A secret key of 4.1 kbps and 1.06 Mbps for DV- and CV-QKD, respectively. This configuration was chosen to simulate three nodes in a network, where the long distance link relies on the advantage of DV-QKD in tolerating channel loss, and the short distance link exploits CV-QKD to achieve a high secret key rate. A metropolitan network could use CV-QKD as short links can benefit from the reduced price of the receivers (no need of single photon detectors) and the coexistence capabilities with classical data channels, while DV-QKD could cover longer links.
Besides the configuration with receivers placed at two different locations, one could consider a network where each node have DV- and CV-QKD receivers and transmitters, and the network controller would choose the technology that maximizes the performance of the QKD depending on the link parameters. We remark that DV- and CV-QKD receivers could be combined into the same system by using two different detector types (single photon and coherent detectors).
In addition to the BB84 DV- and GG02 CV-QKD protocols demonstrated here, the transmitter could allow for implementing other protocols by changing the electrical patterns via software. For instance, the Distributed Phase Reference DV-QKD [45,46], and CV-QKD with discrete modulation [47]. These results are an initial demonstration of an adaptable QKD transmitter and network. The performance and the maximum achievable distance for DV and CV-QKD can be significantly improved for instance by increasing the clock rate (DV and CV), using shorter detection windows to minimize dark counts (DV), reducing reference pulses overhead (CV and DV), single photon detectors with lower dark counts (DV), or lower noise balanced detector (CV). We note that the present transmitter is based on of-the-shelf telecommunication components, with similar hardware as CV-QKD transmitters shown in Refs. [9,14,43]. Therefore, enabling for a combined DV and CV-QKD transmitter would not represent a significant increase in cost compared to a CV-QKD only transmitter. Furthermore, in this work, the asymptotic limit was used to obtain an estimation of the possible secret key rate. However, in a future QKD implementation, finite-size effects [48,49] and key reconciliation [2,8] may also be considered to extract a final secret key.
The presented versatile transmitter could represent a suitable and convenient platform for integrating QKD in modern software defined networks. Exploiting complementary advantages of DV- and CV-QKD schemes, the flexibility and applicability of QKD can be extended, fostering the technology deployment.
Funding
Horizon 2020 Framework Programme (820466); Fundación Cellex; Fundacio Mir-Puig and Departament de Politiques Digitals i Administracio Publica; Generalitat de Catalunya (CERCA); Agencia Estatal de Investigación ( TUNA-SURF PID2019-106892RB-100); Vetenskapsrådet (International postdoc grant); H2020 Marie Skłodowska-Curie Actions; Agència de Gestió d'Ajuts Universitaris i de Recerca (2017 SGR 1634); Departament de Politiques Digitalis i Administracio Publica (SmartCAT).
Disclosures
IL, SE and VP are co-inventor of a patent application related to the content of this paper.
Data availability
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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