High-speed measurement-device-independent quantum key distribution with integrated silicon photonics

Measurement-device-independent quantum key distribution (MDI-QKD) removes all detector side channels and enables secure QKD with an untrusted relay. It is suitable for building a star-type quantum access network, where the complicated and expensive measurement devices are placed in the central untrusted relay and each user requires only a low-cost transmitter, such as an integrated photonic chip. Here, we experimentally demonstrate a 1.25 GHz silicon photonic chip-based MDI-QKD system using polarization encoding. The photonic chip transmitters integrate the necessary encoding components for a standard QKD source. We implement random modulations of polarization states and decoy intensities, and demonstrate a finite-key secret rate of 31 bps over 36 dB channel loss (or 180 km standard fiber). This key rate is higher than state-of-the-art MDI-QKD experiments. The results show that silicon photonic chip-based MDI-QKD, benefiting from miniaturization, low-cost manufacture and compatibility with CMOS microelectronics, is a promising solution for future quantum secure networks.

The combination of silicon photonic chips and MDI-QKD enables a remarkably new networkcentric 3 or quantum-access 2 structure with an untrusted relay. In such a structure (see Fig. 1b), each user only needs a compact transmitter chip, whereas the relay holds the expensive and bulky measurement system (and quantum memory 30 ) which are shared by all users. Importantly, this structure can by-pass the challenging technique for intergrading single-photon detectors on chip 31, 32 , since the users do not need to do the quantum detection. Overall, the chip-based MDI-QKD network is a promising solution for low-cost, scalable QKD networks with an untrusted relay.
Here, we experimentally demonstrate a 1.25 GHz, silicon-chip-based, polarization-encoding MDI-QKD system. Each user possesses a photonic chip transmitter, which integrates the QKD encoding components of intensity modulator, polarization modulator and variable optical attenuator. The chips are manufactured by standard Si photonic platforms, packaged with thermoelectric cooler (TEC), and designed compactly for the purpose of commercial production. With two chip transmitters, we implement MDI-QKD with random modulations of decoy intensities and polarization qubits, and demonstrate a finite-key secret rate of 31 bps over 36 dB channel loss. In addition, we obtain a key rate of 497 bps over 140 km commercial fibre spools. The achieved key rate is higher than those of previous MDI-QKD experiments [13][14][15][16][17][18][19] (see Table 1).
Setup. Figure 2a shows the schematic of our chip-based MDI-QKD experiment. Using pulsed laser seeding technology 33 where a master gain-switched laser (Master) injects photons into the cavity of a slave gain-switched laser (Slave) through a circulator (Circ), Alice and Bob each generates low-jitter phase-randomized light pulses at a repetition rate of 1.25 GHz and a center wavelength of 1550 nm. The generated pulses are pass through a 10 GHz bandwidth filter to remove noise. With these sources, we observe stable Hong-Ou-Mandel interference with a visibility up to 48.4% (See Methods).
The generated pulses are coupled into a Si photonic transmitter chip which integrates together an intensity modulator, a polarization modulator and a variable optical attenuator. The components are realized by an in-house design 34 comprising several interferometric structures (see Fig. 2b) which exploit standard building blocks offered by the IMEC foundry. The multi-mode interference (MMI) couplers act as symmetric beam splitters, and the thermo-optics modulators (TOMs) with ∼KHz bandwidth, and carrier-depletion modulators (CDMs) with ∼GHz bandwidth act as phase modulators. Specifically, the intensity modulator, which is used to generate decoy state with different intensities, is realized by the first Mach-Zehnder interferometer (MZI) containing both TOMs and CDMs. The next components is the VOA, consisting of a p-i-n (PIN) diode for current injection across-section of the Si waveguide and being used to attenuated the pulses to single-photon levels. The tunable attenuation is controlled by applying differential biased voltage to the TOMs with an attenuation up to 110 dB. The output of VOA is connected to the polarization modulator (POL) which is realized by combining an inner MZI with two external CDMs ending in polarization rotator combiner (PRC). The POL can prepare the four BB84 states, |ψ = (|H + e iθ |V )/ √ 2, θ ∈ {0, π/2, π, 3π/2}. Further details involving with the principle of the design can be found in Methods.
The chip has a footprint size of 4.8 × 3 mm 2 and is packaged with a commercial TEC. A precision and compact temperature controller is designed to drive the TEC. With this design, the chip provides a stable polarization encoding and decoy-state modulation. The observed quantum bit error rate (QBER) maintains at low values over several hours of operation (See Fig. 3). The packaged chip with a total volume of 20 × 11 × 5 mm 3 is soldered to a standard 9 × 7 cm 2 printed circuit board, as shown in Fig. 2c. With dedicated layout, the chip is easily assembled by using commercial foundry, providing a low-cost, portable, stable and miniaturized device for MDI-QKD.
To realize MDI-QKD, Alice and Bob send their encoding pulses to Charlie, who performs a BSM on the incoming pluses. Charlie's measurement setup comprises a 50/50 beam splitter (BS), two electronics polarisation controllers (EPCs), two polarising beam splitters and four superconducting nanowire single photon detectors (SNSPDs, detection efficiency ∼53%, dark counts ∼50 Hz). The detection events are registered using a high-speed time tagger where a successful coincidence induces a projection into one of the two Bell states |ψ ± = 1 √ 2( |HV ± |HV ).
For high-rate MDI-QKD, an important part is the high-speed electronics for control and synchronization. In our experiment, Alice and Bob each uses a home-made cost-effective FPGA board to accomplish all electrical controls, including driving the laser, randomly modulating IMs and POLs, synchronizing all stations, etc. The specialised electronics enable us to take advantage of the small size of the chips towards a compact MDI-QKD system. To share a common polarisation reference between Alice and Bob, as well as compensate the polarisation drift in the quantum channel, we develop an automatic polarisation alignment with electronic polarisation controllers, which can rapidly calibrate the polarisation reference (see Supplementary).

Results.
We experimentally characterise each of components in the chip. The bandwidth of the CDM reaches ∼21 GHz which is measured by using a vector network analyzer. The IM provides a static extinction ratio (ER) of ∼30 dB and a dynamic ER of ∼20 dB. We characterize the produced polarisation state with measurement devices in Charlie. The EPCs are adjusted so that each PBS is aligned to rectilinear and diagonal bases, respectively. We obtain an average polarization ER of ∼23 dB. The attenuation of the VOA is ranging from 0 to ∼110 dB. The performance of the chip is sufficient for a low-error, high-rate MDI-QKD (see Supplementary).
Using the described set-up, we perform a series of MDI-QKD experiments using the fourintensity decoy-state protocol 35 . Finite-key effects are carefully addressed using the standard error analysis approach 36 . In the finite-key scenario 37 with a failure probability of 10 −10 , we perform a full optimization of the implementation parameters by exploiting the joint constrains for statistical fluctuations 35 (see Supplementary). The experimental results are plotted in Fig. 3 and Fig. 4. The data points are first collected by using optical attenuators to emulate the attenuation of standard single mode fibres (0.2 dB/km). We obtain an average QBER of ∼2.8% (27.1%) in Z (X) basis. At the total loss of 28 dB (corresponding to 140 km fibre), we run the system for 7.7 hours and send a total of 3 × 10 13 pulse pairs from each client. The finite-key secret rate is 268 bps. At the total loss of 36 dB (corresponding to 180 km fibre), to maximize the key rate, we slightly enhance the bias current of SNSPDs, resulting in a higher detection efficiency (62%) but a lower maximum counting rate. We achieve a finite-key secret rate of 31 bps in 10 hours of system operation time. Next, we replace the optical attenuators with two commercial fibre spools of 70 km each (corresponding to ∼27 dB tota loss), and obtain an asymptotic secret key rate of 497 bps which is close to the finite-key one obtained from the optical attenuators (see Supplementary).
To illustrate the progress entailed by our results, we include in Fig. 4 the highest key rate of selection of existing MDI-QKD experiments. See Table 1 for a detail comparison of different parameters. Although a GHz MDI-QKD was reported in ref. 15 , the implementation of random modulations of decoy intensities and polarization states was not demonstrated there. In this sense, apart from the chip-based implementation, our experiment is the first GHz MDI-QKD with random modulations, and also, it represents the highest key rate for MDI-QKD.
Discussions. We have demonstrated a high-speed chip-based MDI-QKD system where both clients possess a low-cost Si photonic transmitter chip. The transmitter can be further integrated with the laser on a monolithic chip 38, 39 or via wire-bounding. We perform a complete demonstration of polarization-encoding MDI-QKD and distill finite-key secret rates higher than previous experiment. This work paves the way for low-cost, wafer-scale manufactured MDI-QKD system, and represents a key step towards building quantum network with untrusted relays 2, 3, 40 .
Notes added: When we prepare the manuscript, we become aware of a related work in ref. 41  Si transmitter chip The generated pulses are coupled into a Si photonic transmitter chip which integrates together an intensity modulator, and polarization modulator, and variable optical attenuator. The intensity modulator is realized by the first Mach-Zehnder interferometer. By applying multi-level RF signal to the CDMs, the intensities are randomly modulated according to four different intensity choices (µ , ν, ω, 0). The intensity modulator provides a static extinction ratio (ER) of ∼30 dB and a dynamic ER of ∼ 20 dB. To reduce the QBER penalty from the ER, we use an external LiNbO 3 intensity modulator to enhance the ER of vacuum state.
The next components is the VOA, consisting of a PIN diode for current injection acrosssection of the waveguide and being used to attenuated the pulses to single-photon levels. In our chip, we have three cascade connected VOAs and each VOA provide a ∼38 dB dynamic range.
By applying differential dc-biased voltage to the PIN, the max attenuation is up to ∼110 dB. The We characterize the produced state by using the measurement device in Charlie. The EPCs are adjusted so that each PBS is aligned to rectilinear and diagonal bases, respectively. With RF voltages between 0 and 7.5 V, we obtain an average polarization ER of ∼23 dB which is sufficient for a low-error MDI-QKD operation.
Detection The Bell state measurement devices are located in Charlie. The synchronization clock is electrically distributed with a tunable time delay in steps of 1 ps. This enables Alice, Bob and Charlie to electrically compensate any temporal drifts. The projection results are detected with four SNSPDs. The SNSPDs is cooled down to 2.1 K and with an detection efficiency of ∼53%, dead time of ∼40 ns, time jitter of ∼70 ps and dark counts ∼50 Hz. Since the system has a GHz repetition rate, which requires that the SNSPD can tolerate a peak counting rate of more than 5 MHz. We solve it by inserting a 50 ohm shunt resistor between the dc arm of the bias tee and the ground at room temperature. This improved electrical configuration can prevent the detector from latching at a higher count rate without scarifying the detection efficiency. The detection events are recorded by a high speed time tagger with a max data transfer rate up to 65 MHz. The time coincidence time window is set to 600 ps which is an optimal trade-off between the detection efficiency and the error rate of X basis.    are combined and treated together, as proposed in ref. 35 . This can produce a higher key rate than independent constrains. Finally, the secret key is extracted using the formula, where Q Z ss and E Z ss are the gain and quantum bit error rate QBER in the Z (signal) basis, P s A (P s B ) is the probability of signal state for Alice (Bob), Y X,L

11
and e X,U

11
are the lower bound of singlephoton yield and the upper bound of QBER, estimated by the decoy state statistics in the X basis, h is the binary entropy function, and f e is the error-correction efficiency, which is set to 1.16.
Experimental details.
Source. In our setup, Alice and Bob each generates the 1.25-GHz laser pulses using laser seeding technology. To test the visibility of the setup, we perform a two-photon Hong-Ou-Mandel inter-ference experiment. The electronic polarisation controllers (EPCs) in Charlie are adjusted so that each polarised beam splitter (PBS) is aligned to rectilinear basis. The photon count rate is attenuated to ∼ 3.5 MHz per detector. Data is collected for 100 s with a coincidence time window of 600 ps. As shown in Fig. 5, we obtain a visibility of 48.4%.
Si chip transmitter. A CDM, acting as a phase modulator, is a key component in our chip. The bandwidth of the CDM must be subtly estimated since it has a crucial role on the performance of intensity modulators (IMs) and polarization modulators (Pols). We measure the bandwidth of the CDM by using a vector network analyzer. As shown in Fig. 6, we achieve an 3-dB bandwidth of ∼21 GHz.
Alice and Bob each needs to prepare laser pulses in four intensities which are realized by the intensity modulator on the chip. In experimental characterization, a static extinction ratio (ER) of 29.7 dB is achieved with an applied dc-voltage of 0.97 V. In the dynamic ER test, we first trigger the IMs with 625-MHz RF signals and get an ER of 21.5 dB. Then, we enhance the repetition rate of RF signals to 1.25-GHz, and an ER of 19.8 dB is obtained. The decline of the ERs with rising repetition rate is caused by electronic jitter. To further test its performance, we randomly drive the IM with four different RF voltages at a repetition rate of 1.25 GHz, which are generated by our home-made FPGA control board (See Fig. 12). As shown in Fig. 7, the four voltage levels produce four intensities which can be used for signal state (s) and three decoy states (µ, ν, ω).
A variable optical attenuation (VOA) is realized by using a p-i-n (PIN) diode structure where a PIN diode is designed for current injection across-section of the waveguide. In our chip, we have three cascade connected VOAs. Figure 8 shows the tuning ranges of one of the VOAs, which could provide 38.0 dB of attenuation. By applying differential dc-biased voltage to the PIN on each VOA, the max attenuation is up to ∼110 dB which is sufficient to attenuate laser pluses to single-photon levels.
A polarization modulator is used to prepare the four states in conjugate bases, e. g., the key We first characterize the produced states by using a polarimeter system (Thorlabs PAX1000).
As shown in Fig. 9, with appropriate RF signals, we prepare four polarized states in conjugate bases, exhibiting a well ER (∼26 dB) and a high degree of polarization (∼0.993). Then, we measure the produced states with the measurement device in Charlie. The EPCs are adjusted so that each PBS is aligned to rectilinear and diagonal bases, respectively. With RF voltages between 0 and 7.5 V, we obtain an average polarization ER of ∼23 dB which is sufficient for a low-error MDI-QKD operation.
Polarization alignment. Alice and Bob need to share a common polarisation reference as well as compensate the polarisation drift in the quantum channel. Here, we develop an automatic polarisation alignment method which rapidly calibrates the polarisation reference. Figure 10 shows the schematic of our alignment system, which is extracted from the setup in the main text. The system can be summarized in the following three steps, which can be realized by following the flowchart in Fig. 11.
Step 1: Bob and Charlie share a common reference by adjusting EPC-1 and EPC-2, following the flowchart in Fig. 11(a).
Step 2: Alice aligns her bases by adjusting EPC-A, following the flowchart in Fig. 11(b).
Step 3: Charlie align one of PBS to the Z-basis by adjusting EPC-2, following the flowchart in Fig. 11(c).
At last, Alice, Bob and Charlie automatically share a common polarization reference at a short time.
Electronic control board. Figure 12 shows the architecture of the FPGA board, which mainly consists of memory module, serial/parallel conversion module (S/P conversion), delay module, thermoelectric cooler (TEC) module, synchronization module (Syn) and analogs output module.
All the modules (except the analogs output module) are implemented on a Xilinx Kintex-7 FPGA.
8 digital channels are able to generate signals with 10 GHz sampling rate. Among them, two sets of channels (3,4,5 and 6,7,8) are synthesized to output multi-level signals for driving IM and Pol, respectively. After being amplified to 8 V, the analog outputs reach a bandwidth of 2.5 GHz thanks to the careful impedance matching.
The memory module provides 64 kb for 8 digital channels each to storage waveform. The S/P conversion module is used to convert the the low-speed serial data to high-speed parallel data.
With this conversion, the data transmission rate reaches 12.5 Gbps, which meets the requirement