Quantum key distribution (QKD) has been believed as a promising tool providing theoretic information security without any restrict on the eavesdropper’s computing power. Since the first QKD scheme, named BB84 protocol [1], was proposed by Bennett and Brassard in 1984, QKD has attracted a lot of interests and achieved a rapid development. So far, several QKD theoretical schemes have been proposed to improve performance or enhance security [2–9]. Experimentally, QKD has been widely implemented toward long distances [10], GHz repetition rates [11,12], field tests [13], and large-scale networks [14,15]. The recording transmission distance of QKD was pushed up to 830 km installed fiber [16]. Recently, important breakthroughs were achieved in the demonstration of device-independent QKD [17–19]. Recent researches have focused on making QKD systems simpler, more compact, and lower-cost for widespread deployment [20,21].

Integrated photonics is a natural solution to realize miniature QKD [22,23]. In particular, QKD chips relying on well-established integrated techniques have been fabricated to realize key QKD devices [24–28]. The reliability of chip-based QKD devices has also been demonstrated by implementing several QKD protocols, including decoy-state BB84 [27,29–35], high dimensions [36,37], continuous variables [38], and measurement-device-independent QKD [39–42]. These achievements open the way to implant QKD into telecommunication networks. See Ref. [43] for a recent review for advance in chip-based QKD.

Until now, however, chip-based QKD experiments have two substantial limitations. First, although remarkable advances in quantum integrated devices enable chip-based demonstration of QKD, it requires additional off-chip hardware to perform auxiliary tasks in the process. For example, in a recently reported multichip QKD system [44], the time synchronization between Alice and Bob is realized using an additional classical light synchronization setup. In the photonics polarization decoder presented in Ref. [34], a bulk fiber-based polarization controller is used to track polarization basis and to compensate polarization drift.

Second, despite that standard silicon photonic fabrication provides a feasible way to realize mutlifunctional devices for manipulation of quantum states, it is hard to fabricate some integrated components for quantum applications. For example, some prior works involving chip-based polarization-encoding systems still use discrete optics devices to demodulate the quantum states due to the difficulty of achieving integrated polarization manipulation devices [29,31,33,40]. Hence, building a fully deployed QKD system is still challenging.

In this work, we present a resource-efficient chip-based polarization-encoding QKD scheme in which key distribution and all auxiliary tasks are realized using the same chip devices. The scheme is implemented using a chip-based encoder and a decoder that are manufactured by a standard Si photonic platform. The time synchronization and polarization drift compensation are performed exploiting a qubit-based method, which relies on the quantum states generated by the chip devices. The scheme experimentally shows an average quantum bit error rate (QBER) of 0.50%±0.02% and high stability in the 6 h continuous operation. Furthermore, we successfully generate secure bits over different fiber channel lengths, up to 150 km fiber spool with a finite key rate of 866 bit/s. This study paves the way for low-cost, wafer-scale manufactured QKD systems and provides a promising solution for making chip-based systems simple.

Our chip-based BB84 QKD system is schematically shown in Fig. 1. Alice prepares decoy-state BB84 polarization states on a chip-based transmitter and distributes the states to Bob, who possesses a chip-based receiver, via an optical fiber link.

Alice generates low-jitter phase-randomized light pulses at a repetition rate of 50 MHz and a center wavelength of 1550 nm. The generated pulses are coupled into a Si photonic encoder chip [see Fig. 1(b)], which integrates together an intensity modulator (IM) and a path-to-polarization modulator (Pol-M). The components consist of interferometric structures, which exploit standard building blocks offered by the commercial fabrication foundry. The multimode interference (MMI) couplers act as symmetric beam splitters, and the thermo-optics phase shifters (PSs) with ∼5kHz bandwidth and the carrier-depletion modulators (CDMs) with ∼5GHz bandwidth act as phase modulators.

The first interferometric structure, realizing a Mach–Zehnder interferometer (MZI), is used to realize an IM. The IM is used to generate different intensities, one intensity μ for signal state and another one ν for decoy state. The ratio μ/ν is set by both DC-bias of the PSs and the RF signals sent to the CDMs of the MZI.

The output of IM is connected to Pol-M, which functions by means of a path-to-polarization converter. The structure combines an inner MZI with two external CDMs, ending in a two-dimensional grating coupler (2-D). The 2-D, acting as a polarization rotator combiner, converts the path-encoding information at each arm of the MZI into polarization-encoding information at the output. The Pol-M enables the preparation of the four BB84 polarization states, |ψ⟩=(|H⟩+eiθ|V⟩)/2,θ∈{0,π/2,π,3π/2}, where θ∈{0,π} (θ∈{π/2,3π/2}) represents the states in Z (X) basis. More details about chip design as well as work principle can be found in Ref. [33].

All the operation of Alice’s devices, including triggering the laser and applying voltage on the IM and Pol-M, is controlled by arbitrary waveform generators (AWGs) and homemade time delay generators (Delayer). Alice’s encoding pulses are sent to the silicon-based measurement setup in Bob.

The transmitted signals are coupled into Bob’s decoder chip [see Fig. 1(c)] via spot-size converter (SSC). The decoder chip then converts the polarization-encoding photons to the on-chip path encoding via a polarization splitter-rotator (PSR). Therefore, these photons passively choose the measurement bases of Z or X via a symmetric MMI. The quantum measurement in Z(X) base is constituted by a polarization controller measurement state PC1 (PC2). Each PC contains two MMIs and four thermal PSs. By fine-tuning the applied voltages, supplied by a DC power supply, on PSs, the PC1 and PC2 constitute the quantum measurement in Z and X basis, respectively. Further information about the principle of the polarization state analysis by the decoder chip for the BB84 protocol can be found in Ref. [45].

After configuring the measurement basis in PCs, the photons are detected by four commercial superconducting nanowire single photon detectors (SNSPDs, Photon Technology Co., Ltd.). The SNSPDs are cooled down to 2.1 K and have an detection efficiency of around 75%, dead time of ∼40ns, time jitter of ∼70ps, and dark counts of ∼25Hz. The detection events are registered using a high-speed time tagger (Timetagger20, Swabian Instruments). The local clock reference for Bob is generated by using the internal clock in the time digital converter (TDC). A laptop then reads the TDC data and processes it for time synchronization and polarization drift compensation. The encoder is triggered by a programmable DC power supply.

The encoder and decoder chips are fabricated using stand silicon photonics foundry services with an in-house design. The encoder and decoder have a footprint size of 6mm×3mm and 1.6mm×1.7mm, respectively. The encoder chip is butterfly packaged with a total volume of 20mm×11mm×5mm and then soldered to a standard 9cm×7cm printed circuit board, as shown in Fig. 1(d). The decoder chip is packaged using a chip-in-board assembly with a total volume of 3.95cm×2.19cm×0.90cm, as shown in Fig. 1(e). With a dedicated layout, the chip is easily assembled by a commercial foundry, providing a low-cost, portable, stable, and miniaturized device. Details for the encoder and decoder chip designs and fabrications can be found in Appendix A.

Different from the conventional optical or electrical time synchronization methods, we apply a qubit-based method to synchronize two remote users’ clocks. This method enables synchronizing the clocks using the transmitted quantum signal states. This means that our setup does not require a synchronization subsystem, which normally consists of a pulsed laser and a photonic detector, as utilized in pioneering works [46–48]. We remark that removing the synchronization subsystem is extremely crucial for building a fully chip-based QKD system since the development of an on-chip laser source remains a great challenge on Si photonics research [49].

The main goal of the time synchronization is to recover the specific frequency of the qubits arriving at the detectors and the time-offset of corresponding qubits between Alice and Bob. The main idea of our algorithm is similar to a recently proposed Qubit4Sync algorithm [50] except the method of recovering the absolute time-offset; instead of implementing public periodic-correlation codes in the first L states, we divide those codes into single bits and then periodically and cyclically embed them in prepared states. The detailed description of our synchronization method is presented in Appendix B. Here, we describe the main features of our algorithm as follows.

Our approach first computes the frequency from the time-of-arrival measurements based on fast Fourier transform. To recover the absolute time-offset, Alice prepares a random qubit string, which is periodically and cyclically embedded with several public known bits from periodic-correlation codes with a length of L. Then each bit, according to a preset ratio M, is sequentially inserted into random encode bits. For example, supposing that M=9:1, every 10 bits contain 9 random bits that are embedded with a single bit from periodic-correlation codes of length L. When the L bits are consumed, the periodic-correlation codes are cyclically reused. By correlating these periodic-correlation codes with the one received by Bob, it is possible to distinguish which state received by Bob is the first one sent by Alice. The absolute time-offset of the first qubit can be obviously derived. This is the typical frame-synchronization technique used in digital communication systems [51].

Our algorithm periodically inserts the synchronization string in the random data stream so that Bob can execute the qubit synchronization algorithm at any time and quickly reestablish synchronization when the system is out of step. This allows the system to continuously accumulate the bit string for a long time up to 6 h.

After recovery time synchronization, we can further perform polarization compensation using a shared qubit string. We note that, due to the environmental disturbance, the polarization state of the transmitted photon is rotating unpredictably along fiber channel. This polarization variation would lead to a mismatch between Alice and Bob’s reference frames and result in a high QBER and low secure key rate. To eliminate it, a polarization compensation subsystem, which typically includes an auxiliary laser and several electronic polarization controllers, must be utilized.

In our scheme, since the POVMs in the Z and X bases are set by actively tuning PSs at the stages of PC1 or PC2, this enables the polarization basis tracking and, hence, allows our system to compensate polarization rotation.

Here, similar to the work in Refs. [20,52], we use a qubit-based polarization compensation method that employs a shared qubit string. The shared qubit strings are generated using the chip-based transmitter and receiver; hence, it does not need additional hardware. The idea is that Bob directly evaluates the QBER in Z and X basis from the public string after performing the time synchronization process. The estimated QBERs are then put into an optimization algorithm (based on gradient descent algorithm), which is running in Bob’s laptop. The laptop then adjusts the applied voltages of PS in PC1 and PC2 using a programmable linear DC source. Taking advantage of the gradient descent optimization algorithm, the voltages applied on PSs in PC1 and PC2 are tuned in real time to suppress QBER. The process is continuously running until the estimated QBER is lower than the preset threshold.

We first experimentally characterize each component in the encoder chip. At a frequency of 50 MHz, the IM provides a static extinction ratio (ER) of approximately 27 dB and a dynamic ER of approximately 18 dB, which meets the requirement of the one-decoy method [53]. The produced polarization states are analyzed with the decoder by Bob. The PCs are calibrated to Z (X) basis. We obtain an average polarization ER of ∼23dB. The performance of the chip ensures realizing a low-error, high-rate QKD system.

The 3 dB bandwidths of CDM and PS, which are key parameters evaluating the performance of the IM, Pols and PC, are measured. The 3 dB bandwidth of CDM is tested by measuring the eye diagram, and a value of approximately 10 GHz is obtained, which is consistent with design. The 3 dB bandwidth of PSs is approximately 3 kHz. This value ensures that the decoder has a fast polarization tracking speed in field-buried and aerial fibers.

The total loss of the decoder chip is approximately 4.6 dB. The source of loss includes coupling-in and -out loss (∼3dB), as well as on-chip device propagation loss (∼1.6dB). The MMI and waveguide bends contribute mostly to the propagation loss. The loss in the decoder chip reduces the probability of detecting photons, thus compromising the secure bit rate of the QKD system.

We first report the intrinsic QBER and stability of our QKD setup, which gives a quantitative first look of the performance of our setup. Furthermore, the characterization is crucial to predict the secure key rate under different channels or detector technologies. We first remove the fiber spool and then send a sequence of qubits prepared using the method described in Section 2. The total length of periodic-correlation codes L=5×104 and the ratio M is set to 9:1. The transmitted states are analyzed, including time synchronization performance as well as QBER estimation, using the measurement devices in Bob. The intensity of signal μ is set to a constant value of 0.5. The experimental results are shown in Fig. 2, which shows, in a 6 h testing time, an average QBERz is measured to be 0.78%±0.02% for the Z basis, while for X basis, the average QBERx is 0.22%±0.04%. The total QBER for both two bases is 0.50%±0.02%. These results demonstrate the low intrinsic QBER and high stability of our setup. Due to different applied voltages on CDMs for the preparation of the four polarization states, the phase-dependent loss characteristics and saturation of the CDMs result in a discrepancy in the QBERs of Z and X. Since the data are contentiously collected, these results demonstrate the time synchronization method works well in a long-time run.

To test the performance of the polarization compensation method, we continuously run the system with a 50 km fiber spool channel. We exploit a fiber polarization scrambler, of which the applied voltages are step-by-step increased 1 V every 5 min, to mimic the polarization rotation of photons in long fiber spool. With our polarization feedback algorithm, we are able to compensate the polarization drifting to a low QBER within 1 min. For comparison, we also measure the QBERs without activating the polarization feedback.

The experimental results are shown in Fig. 3. It can be observed that, for 2.4 h continuous run, due to the polarization drift introduced by the environmental distance and polarization scrambler, the QBERs for Z and X basis gradually increase to 50% without active polarization feedback. In this stage, no secure key bits can be extracted. In contrast, with our polarization feedback process, the QBERs keep stable and stay at a low level of around 0.85% for 2.4 h run.

Using the described setup, we perform a series of one-decoy QKD experiments with different fiber spool lengths of 50 km, 100 km, and 150 km. To get a better performance, we perform a full optimization of the implementation parameters for the one decoy-state protocol [54]. For example, in the scenario of 100 km, the intensities of the signal states and decoy state are chosen to be μ=0.565 and ν=0.143, respectively. The probabilities of sending out the signal state μ and choosing the bases Z are Pμ=0.798 and Pz=0.944, respectively. At Bob’s side, the probabilities of choosing the measurement basis in Z and X are permanently set to be equal due to the balanced MMI used in the decoder.

For each distance, the total length of periodic-correlation codes is of 5×104, and the ratio M is set to 9:1. We continuously accumulate the detection numbers nz of approximately 107 and perform the finite key analysis using [53] $$\begin{gathered} R≤(sz,0L+sz,1L(1−h(ϕzU))−leakEC \\ −6log2(19/ϵsec)−log2(2/ϵcor))/t, \end{gathered}$$(1)where t is the time duration of each acquisition, sz,0L is the lower bound of the detector event received by Bob when Alice sends a vacuum state in Z basis, and sz,1L is the lower bound of the detection event, given that Alice only sends a single-photon state in the Z-basis. ϕzU is the upper bound of the phase error rate, leakEC is the number of bits consumed for error correction, and ϵsec and ϵcor are the parameters used to evaluate secrecy and correctness, respectively. The h(x) denotes the Shannon binary information function.

An overview of experimental parameters and performances for different distances is listed in Table 1. The experimental results are also plotted in Fig. 4. It can been seen that we successfully run QKD up to 150 km; with a continuous accumulated time of 3640.4 s, a finite key rate of 866 bit/s is obtained. These results also demonstrate that our qubit-based synchronization and polarization compensation methods work well even in a high loss fiber channel and a long running time. The detailed experimental results are listed in Appendix C.Table 1.

Overview of Experimental Parameters and Performances for Different Distances^a

We have demonstrated a resource-efficient fully chip-based BB84 QKD scheme. The scheme implemented the time synchronization and polarization compensation using on-chip devices, which generates also secure keys for quantum communication. The system can distill a finite key secure bit rate of 866 bit/s over up to 150 km fiber spool. Limited by the driving circuit, which only supplies maximum peak-to-peak voltage Vpp=10V at a repetition rate of 50 MHz, the current system works at a repetition rate of 50 MHz and has a relatively low key rate. The obtained key rate can be further increased by using a state-of-the-art high-speed modulator driving circuit [55]. The presented system can be further integrated with the laser based on wire-bounding or the hybrid integration technologies [56,57], which contributes to a compact chip-scale QKD transmitter. Since CDMs are used to modulate the phase, it inevitably introduces the phase-dependent losses. To solve this problem, a polarization-loss-tolerant protocol [58,59] can be incorporated into our work, or novel phase modulation schemes provided in Refs. [28,48,60] can be employed. This work paves the way for a low-cost, robust wafer-scale manufactured QKD system and provides a promising scheme for developing simple chip-based systems.

Note: During the preparation of this manuscript, the authors noticed that a related work which presented a high-speed integrated QKD system [61] has been released. Although both works involve the chip-based QKD system, there are several differences. First, in contrast to the use of a time-bin encoding scheme, our work employs a polarization encoding scheme, which does not require the maintenance of interferometric stability that would be necessary in time-bin encoding. Additionally, polarization encoding is also a favored choice for the deployment of quantum networks and free-space QKD, especially for ground-to-satellite QKD.

Second, the receiver chip in Ref. [61] was fabricated on an aluminum borosilicate glass process platform, whereas we use CMOS-compatible silicon photonics technology, which has advantages of high-density integration and mature fabrication processing. Third, Ref. [61] realized synchronization by using classical communication between two field-programmable gate arrays (FPGAs), while our work uses a low-cost and efficient qubit synchronization approach.

Acknowledgment. We thank Shizhuo Li for drawing the diagram of the chip.

Author Contributions. K. W. designed and developed the experiment. X. Hu, X. Hua, and X. X. developed the device design and fabrication. K. W., Y. D., Z. Z, C. H., and Y. C. implemented the experiment and evaluated the data. K. W. and X. X. supervised the research and experiment. All authors contributed to the writing of the paper.