Security communication is an indispensable part of government affairs, commerce, national defense and personal daily life. The security of traditional public-key cryptography, which depends on the computational complexity of certain mathematical functions¹, is gravely threatened by the development of quantum computing science^2⇓-4. The security of quantum key distribution (QKD) is based on the fundamental laws of quantum mechanics and has become a key solution for ensuring information security in the information era⁵.

Since Bennett and Brassard proposed the first quantum cryptography protocol (BB84) in 1984⁶, great progress has been maded in QKD experiments, and numerous experiments have been performed with different degrees of freedom in photons, such as the time-bin phase^7⇓⇓-10 and polarization^{11, 12} over fiber-based^{13⇓⇓⇓-17}, free space^18⇓-20, and underwater^{21, 22} channels. QKD networks have also been deployed worldwide^{23⇓⇓⇓⇓-28}. In order to realize intercontinental secure communications, satellites have been used as trusted relays to connect remote user nodes²⁹, and large-scale satellite networks³⁰ have also been successfully constructed. Furthermore, recent progress in QKD has also been observed in the latest researches^31,32.

In order to apply the increasingly mature QKD technology to the standard communication networks, it is of great importantance to develop a stable, simple, inexpensive and miniaturized QKD system. As the leading platform of quantum photonics technology, silicon photonics exhibit several excellent characteristicsincluding high integration, mature technology and compatibility with complementary metaloxidesemiconductor (CMOS)^33,34. In recent years, silicon-based optoelectronic platforms have been used to develop high-speed, robust, and practical QKD devices. These integrated devices can implement the BB84 protocol^{35⇓⇓⇓⇓⇓-41}, measurement device-independent QKD protocol^42⇓⇓-45, continuous variable QKD protocol⁴⁶, high-dimensional QKD protocol⁴⁷, and coherent one-way and differential phase shift protocols ^39,48. The potential realistic vulnerabilities of chip-based devices have been extensively studied in previous studies^49⇓⇓-52, and a recently published review provides a detailed report on the development of integrated QKD⁵³.

Polarization encoding has been extensively applied in QKD systems over fiber-based or free-space channels. Polarization encoding-based implementations of QKD have been extensively studied using bulk optical components^54,55 or silicon photonics^{35,37,41,56,57}. However, due to the difficulty in realizing polarization conversion by using silicon photonics, previous chip-based devices either utilized bulk optical devices to decode polarization states^35,37,41,56 or employed additional off-chip devices to perform polarization-based tracking or polarization compensation^41,57.

In the current work, a novel silicon-based decoder for polarization-encoding QKD was developed. Based on polarization-to-path conversion method⁵⁸, the chip avoided the requirement of using polarization-independent devices, and realized a polarization state analyzer and polarization compensation for the BB84 protocol without additional hardware. The chip was manufactured using a standard silicon-based photonic platform, and the compact design made it exhibit robustness against environmental disturbances. In an experimental stability test, an average quantum bit error rate (QBER) of 0.59±0.01% was achieved through continuous operation for 10 h without any active feedback. The stability of the chip was further tested by inducing a random fiber polarization scrambler to emulate the polarization drift. The experimental results showed that the decoder could automatically compensate for polarization drift using a developed feedback algorithm. Finally, a proof-of-principle QKD demonstration was performed with a finite-key secret rate of 240 bits per second (bps) over a 100-km fiber spool. Experimental results achieved in the current work demonstrate the feasibility of a silicon-based integrated decoder chip and mark an important step toward a fully integrated polarization-encoding QKD system.

A schematic of the proposed decoder chip is shown in Fig. 1a. The chip was fabricated using a standard silicon photonics foundry with the size of 1.6 × 1.7 mm², as shown in Fig. 1b. It was packaged based on a chip-on-board assembly, with a total volume of 3.95 × 2.19 × 0.90 cm³, as shown in Fig. 1c. The entire decoder chip is composed of the following parts: a spot-size converter (SSC), a polarization splitter-rotator (PSR), two variable optical attenuations (VOAs), and four Mach-Zehnder interferences (MZIs), each of the above contains two multi-mode interferences (MMIs) and two thermal phase shifters (PSs).

A SSC was employed to couple the received randomly polarized signal light into the decoder chip. The PSR then converted the horizontal and vertical components of the polarized signal light into two on-chip single-mode waveguides that propagated as two transverse electric (TE) signals. The variable optical attenuation (VOA) was placed into each arm of the PSR so as to balance the polarization-dependent loss caused by SSC and PSR, which typically have appropriate losses of 0.4 dB and 0.7 dB, respectively.

Each TE signal was then spit by a 1 × 2 multi-mode interferences (MMIs) into either a stage 1 polarization controller (PC1) or stage 2 PC (PC2). Each PC was comprised a phase shifter (PS)-driven Mach-Zehnder interference (MZI) with two additional PSs. The outputs of the PC were coupled with single-photon detectors via the SSC. Further information regarding the working principles of key components and fabrication process of the chip is provided in the section of METHODS.

When carefully controlling the PSs, the outputs of PC1 (PC2) constitute the positive operator value measurements (POVMs) in the Z-basis (X-basis) in the BB84 protocol. Furthermore, the fact that the POVMs are constrained by actively adjusting the PS allows the chip to compensate for variations in the polarization states caused by fiber birefringence. Further information regarding the POVMs by the polarization decoder chip for the BB84 protocol is presented in the part of Supplementary Materials.

A testing platform was built for testing the performance of the chip, as shown in Fig. 2. A commercial laser source (LD, WT-LD, Qasky Co. LTD) with a repetition rate of 50 MHz and a pulse width of 200 ps was employed in the experimental test. The generated light pulses were coupled into the encoder chip, which was composed of an intensity modulator and a polarization modulator, generating decoy states with a dramatic extinction ratio (ER) of ∼18 dB and four polarization states with an average ER of ∼25 dB. The encoder chip modulated the laser pulses and generated quantum states at a repetition rate of 50 MHz. Subsequently, the modulated quantum states were attenuated to the single-photon level by off-chip variable optical attenuation (DA-100, OZ Optics Ltd.) and transmitted to the receiver chipvia a fiber channel. The signals were analyzed using the decoder chip and then detected by an off-chip single-photon detector (SPDs, WT-SPD2000, Qasky Co. LTD.) with a detection efficiency of 10% and a dark count rate of 400 Hz. A time-to-digital converter (TDC, quTAG100, qutools GmbH) was adopted to record the final detection events, and a personal computer was employed to process the data recorded by the TDC.Characterization of decoder chip Firstly, the decoder chip was characterized. The insertion loss was approximately 4.6 dB, which is comparable to that reported in previous studies^57,59. Further detailed results of the decoder chip insertion loss were listed in Tab. 1. It could be observed that when Alice sends single polarization states (generated by the transmitted chip) $|H〉,|V〉,|D〉$, and $|A〉$, the total losses of decoder chip are 4.14 dB, 4.25 dB, 3.83 dB and 4.57 dB, respectively. Meanwhile, the loss from the fiber incident port to the output ports of H, V, D and A are 4.21 dB, 3.97 dB, 4.20 dB and 4.13 dB, respectively.

The measured modulation range of VOA was distributed from 0 to approximately 3 dB, which is sufficient to compensate for the polarization dependent loss. The 3-dB bandwidth of PSs was approximately 3 kHz, which is sufficient to respond to the polarization variations in field-buried and aerial fibers⁶⁰. The half-wave voltage of the PS, which is a key parameter of the chip, was measured subsequently. Here, measurement of the half-wave voltage of the PS was conducted by measuring the ER of an MZI containing PS (using the same technology as the decoder chip). As shown in Fig. 3, The IM is of a maximum static ER of approximately 26.65 dB and a half-wave voltage PS of approximately 0.72 V.

Finally, testing of the decoder chip's ERs was performed to measure different polarization states. The pulsed light emitted by the laser was coupled into the encoder chip to generate one of the four BB84 polarization states, which was then transmitted to the decoder chip for demodulation. ERs of 28.86 dB, 26.02 dB, 27.70 dB, and 29.21 dB were obtained for the polarization states $|H〉,|V〉,|D〉$ and $|A〉$, respectively.

Inherent stability test In order to demonstrate the reliability of the decoder chip, a 10 h long-term run test was conducted. As shown in Fig. 4, four BB84 polarization states were randomly generated and measured directly using the decoder chip. An average QBER of 0.59±0.01% was obtained through continuous operation for 10 h without any active feedback control. The chip fabricated in the current work exhibited inherent stability, which makes it feasible tobuild a QKD system with a long run time.

Automatic polarization compensation over a 75-km fiber link Here, A polarization compensation scheme which could realize real-time polarization compensation using only shared qubits was developed. It is noted that that the first qubit-based polarization compensation method was introduced in ref.⁶¹ and then perfected in ref.¹¹. The basic idea of the polarization compensation scheme is that Bob evaluates the average QBER in Z- and X-bases (QBER_Z and QBERX) every second. After processing by the feedback algorithm (the algorithm is based on gradient descent⁶²), the computer then controls the programmable linear DC source to change the retardance of θ1, θ2, θ3, and θ4 until QBERZ and QBERX are less than the set threshold. The detailed process of the scheme is described in the part of Supplementary Materials.

In order to test the performance of the polarization compensation scheme, four BB84 polarization states were randomly modulated, in which the probabilities of sending states in Z basis and X basis were 0.9 and 0.1, respectively. Afterwards, the states were attenuated to approximately 0.6 photons per pulse, which were then sent to Bob via a 75-km fiber spool for decoding and detection. Since the polarization drift in an installed fiber is relatively small, a polarization scrambler was placed behind the fiber spool to randomly disturb the polarization of photons entering the decoder chip (the scrambler triggers the time interval randomly within 20-30 min).

The experimental results are presented in Fig. 5. QBERZ, QBERX, and the total QBER of the system are represented by green, blue and red lines, respectively. During the entire 180-min running time, the error rate was increased by more than 50% on average after each perturbation. As shown in the inset of Fig. 5, the average QBER was reduced by the polarization compensation system feedback to approximately 1.59% in about 1 min The polarization could be compensated potentially in much shorter time by optimizing algorithm. The results showed that the polarization compensation scheme is both feasible and robust.

QKD Secure key rates at different fiber distances Finally, a QKD test was performed using fiber distances of 25 km, 50 km, 75 km and 100 km. For each distance, a real one decoy-state protocol⁶³ with optimized parameters was conducted, except for the probability of Bob choosing the Z-basis, and the X-basis was set to 0.5 (owing to the balanced MMI used in the chip).

For each distance, the total number of pulses N=10¹⁰ and the SKR in the finite regime were estimated by the following formulas:

where $s_{z,0}^l$ is the lower bound of the detector event received by Bob, given that Alice sends an empty state under the Z-basis, $s_{z,1}^l$ is Bob receiving the lower bound of the detection event, given that Alice only sends a single-photon state in the Z-basis. ${\varphi }_z^u$ is the upper bound of the phase error rate, ${\lambda }_{\text{EC}}$ is the number of bits disclosed for error correction, and ${ϵ}_{\text{sec}}$ and ${ϵ}_{\text{cor}}$ are the parameters used to evaluate secrecy and correctness, respectively. The $h\left(x\right)=-x{\log }_{2}x-(1-x){\log }_2(1-x)$ denotes the binary Shannon information function.

The experimental results are plotted in Fig. 6. An SKR of 240 bps over 100 km was achieved under a finite-key analysis. The further detailed experimental results for each distance are shown in the part of Supplementary Materials.

In this study, a novel decoder chip for polarization-encoding QKD systems was developed and validated by adopting a silicon-based optoelectronic platform. The receiver chip exhibited high inherent stability, it could also demodulate the polarization states with favorable extinction ratios. Moreover,the chip could automatically perform polarization compensation. In the QKD test, secure key bits were successfully distributed over a fiber distance of up to 100 km.

These results validated the feasibility of implementing polarization decoder chips without an off-chip polarization controller, which marks an important step toward a more compact QKD system⁶⁴. The chip fabricated in the current work would be attractive in different operating scenarios, particularly in an daylight uplinking satellite-based QKD, where the receiver is placed in space and light with 1550 nm wavelength could be exploited^65,66. Furthermore, polarization decoder chip in the current work only requires approximately 2 V voltage for driving PS to achieve polarization state analyzer and compensation, thus electronics design for QKD systems could be dramatically simplified. Further integration of the chip can also be achievedwith hybrid devices technology, in which the optical and electronic components are integrated onto a single microchip.

The spot-size converter consists of a Si waveguide, the width of which is tapered to a narrow tip near the facet⁶⁷. The design of spot-size converter is based on the mode delocalization effect, which increases the spatial distribution of the mode profile along the inverse taper until the mode field size matches the optical fiber mode size. In order to reduce the absorption loss from the buried oxide, the spot-size converter was also set to be suspended.

The polarization splitter rotator includes the following two functional parts: TM₀-TE_n mode converter and TE_n-TE₀ mode converter⁶⁸. The principle of the TM₀-TE_n mode converter is the mode hybridization of the tapered rib waveguides. And the TE_n-TE₀ mode converter was realized by the beam shaping method, which was followed to complete the polarization splitter rotator function.

The chip was fabricated on a standard silicon-on-insulator waferwith a diameter of 200-mm. The wafer consists of a 220-nm silicon layer and a 3-µm buried silica oxide layer based on 90 nm CMOS process from the CompoundTek silicon photonic platform. The width of the single-mode silicon waveguide was 450 nm. The light was coupled into/out of the chip via a SSC with a taper length of approximately 100 µm and then split and converted into TE modes using a compact polarization rotator-splitter⁶⁹.

The VOAs function was based on the forward carrier injection PIN junction, the attenuation of which increased with increasing applied voltage. The length of the VOA is approximately 200 µm. In order to obtain a nearly balanced splitting ratio, the 1 × 2 multimode interferometer (MMI) and 2 × 2 MMI couplers were designed to be approximately 4 × 14 µm² and 8 × 60 µm², respectively. All the eight phase shifters (PSs) are identical, with a length of 260 µm, efficiently resulting in a static extinction of approximately 28 dB when implemented in MZIs. Notably, in real-time, only one PS on one arm in each MZI was active and the other PS was designed for the compensation of a 0.05-dB loss. The pitch of the aluminum DC pad is approximately 150 µm. The pad area is approximately 80 × 100 µm².

Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.chip.2023.100039.

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.

Acknowledgements We would like to express sincere gratitude to Shizhuo Li for drawing the diagram of the chip.

Declaration of Competing Interest The authors declare no competing interests.