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Abstract
The wider deployment of commercial quantum key distribution (QKD) may benefit from an integrated system with reduced cost, small form-of-factor and high robutness. Silicon photonic circuits are good candidates while their performance stability in some contexts remains a challenge. We demonstrate a silicon photonic QKD transceiver based on time-bin protocol. The stability of the transceiver is investigated and a feedback function is proposed to improve the temperature-dependent performance of the transceiver. With the help of a faster data-processing ability, such scheme can facilitate more application scenarios, therefore achieving wider implementation of QKD in the future.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum key distribution (QKD), also known as quantum cryptography, enables two remote parties to share symmetric keys, of which the security is guaranteed by the basic laws of quantum physics [1,2]. For instance, in the BB84 protocol [3], Alice sends single photons randomly encoded in eigenstates of two mutually unbiased bases to Bob, who will recover the information of the states if a correct basis is used during the measurement. According to the quantum no-cloning theorem [4], any eavesdropping actions will cause statistical errors in these results and therefore be found. Combined with the one-time-pad encryption protocol, the unconditioned secure communication between the two parties can thus be realized [5]. To clear away the potential threats on the current cryptosystems by the emergence of quantum computers, enormous efforts have been focused on the realization of large-scale, even global deployments of QKD networks. For instance, various protocols, such as decoy-state QKD and measurement-device-independent (MDI) QKD, have been proposed to overcome the theoretical insecurities caused by imperfect devices [6–8]; improved QKD schemes and encoding methods are used to increase the communication distance as well as the secure key rate [9–13]. On the other hand, more application scenarios, such as portable or pluggable devices, and therefore wider deployments of QKD also rely on stability, cost-reduction and miniaturization of the system. Time-bin QKD protocol encodes quantum states in both the photon’s temporal and phase degree of freedom [14,15]. Compared with the polarization encoding scheme, the time-bin protocol shows better robustness to the turbulence caused by the birefringence in optical fiber channel [16]. Furthermore, only two single-photon detectors and no random number generator are necessary at the receiver, which further eases the cost and complexity of the system.
A prerequisite for the application of the time-bin protocol is the good reproducibility of the delay between the successive time-bins generated by different devices. Benefited from the well-established manufacturing infrastructures for complementary metal-oxide-semiconductor (CMOS), silicon photonics can easily meet such prerequisite while enabling the integrated devices to have small form-of-factors, low power consumption and potentially low costs [17,18]. Recent works have already demonstrated promising applications of silicon photonics on quantum light generation and manipulation [19,20], as well as QKD chips based on various protocols [15,21–24]. While integrated QKD devices have already shown advantages in stability over fiber-based systems [25], serving as a transceiver for the time-bin protocol, silicon photonic circuits suffer an unstable quantum-bit error rate (QBER) due to the large thermal-optic coefficient of silicon [15,26]. This degradation of QBER arises from the misalignment of the reference frame of X and Y bases, which is caused by cumulative phase shifts in the asymmetric Mach-Zehnder interferometers (AMZI). Efforts can be made on the hardware level to inhibit such degradation in QBER: for instance, bulky temperature stabilization systems can be introduced at a cost of increased form-of-factor and complexity of the system; moreover, AMZI structures can be fabricated with sophisticated processes to have low or negative thermal-optic coefficients, compensating for the phase shift [26]. On the other hand, the reference-frame-independent scheme can solve the problem by bounding the knowledge of the keys by an eavesdropper with measurement results of both X and Y bases [27]. Nonetheless, this would require an active selection of the three bases on Bob side.
In this article, we demonstrate a time-bin protocol QKD using highly integrated silicon photonic transceivers. Carrier-depletion modulators are used for a relatively high-speed key generation. A secure key rate of 85.7 kbps at a QBER of 0.84% is achieved for an emulated transmission distance of 20 km in fiber under slow-varying reference frame misalignment (< 0.25$\pi$/min). A delicate feedback process is utilized to maintain the average QBER below a reasonable level while the misalignment of the X basis reference frame fluctuates at a speed around 4$\pi$/min, proving the feasibility of such configurations for practical QKD applications.
2. Experiments
2.1 Silicon photonic QKD transceiver
The highly integrated transceivers were designed and fabricated within a standard multi-wafer project (MPW, Imec) [28], achieving a small footprint of only 3.2 mm $\times$ 5.1 mm. The schematic and microscopic pictures of the transceiver are presented in Figs. 1(a) and 1(b). Two types of modulator are used in the transmitter: thermo-optic modulator (TOM) and travelling wave carrier-depletion modulator (CDM). It is well known that the optical absorption of CDM is aniticorrelated to the magnitude of the reverse voltage [29]. To balance the modulation voltage on each CDM, therefore balancing the deterioration of fidelities of each state, the modulation scheme from [15] is implemented at the transmitter. Specifically, the static working point is configured at $\left \lvert {\mathrm {Y+}}\right \rangle =1/\sqrt {2}(\left \lvert { \mathrm {Z-}}\right \rangle +i\left \lvert { \mathrm {Z+}}\right \rangle )$ by properly setting the TOMs, in which $\left \lvert { \mathrm {Z-}}\right \rangle$ and $\left \lvert { \mathrm {Z+}}\right \rangle$ represent photon states in the early and late time-bin, respectively. Eigenstates of Z or X basis are prepared by applying $V_{\pi /2}$ on a corresponding CDM. As a result, average fidelities of 99.7% and 99.1% are obtained for state preparation and measurement of Z and X basis respectively at a modulation frequency of 100 MHz. In the meantime, benefited from a passive basis-selection scheme in the receiver (i.e. no CDM is needed), the loss of the receiver is only $15$ dB ($5$ dB from the optical input/output), which is nearly 10 dB smaller than that of the transmitter. This will significantly increase the key rate compared with the case when the transmitter serves also as a receiver [15,22]. Figure 2 illustrates the QKD test setup. On Alice side, an off-chip 1550 nm pulsed laser with a FWHM of 50 ps and a repetition rate of 100 MHz is attenuated and coupled into the transceiver. Due to practical limitations of the chip, i.e., a limited chip area and a high $V_{2\pi }$ of CDMs, a phase randomizer is not included in the transceiver. The phase pseudo-randomization from $-\pi$ to $\pi$ is realized by an off-chip lithium niobate phase modulator. Basis signals among $\{\left \lvert { \mathrm {Z-}}\right \rangle , \left \lvert { \mathrm {Z+}}\right \rangle , \left \lvert { \mathrm {X-}}\right \rangle , \left \lvert { \mathrm {X-}}\right \rangle \}$ is pseudo-randomly picked by an synchronized arbitrary wave generator (AWG). On Bob side, a time interval analyzer (TIA) records the time tags of all the detection events from two superconducting single photon detectors (SSPD, efficiency: 70%, dark count rate: 400 cps). The combination of path and relative time information of every detection signal is analyzed by the post-processing program on a computer, which, as a proof-of-concept demonstration, also acts as the classical channel between Alice and Bob.
Fig. 1. Silicon photonic QKD transceiver: (a) Schematic of the silicon photonic QKD transceiver: input laser pulses are attenuated by the MZI-a0 to different intensities as decoy-states; MZI-a1 compensates the extra loss introduced by the longer arm of AMZI-a2, by which each laser pulse is split into two time-bins with equal intensity and a specific phase difference; intensity of the two time-bin pulses is selectively modulated by MZI-a3 to determine $\{\left \lvert { \mathrm {Z-}}\right \rangle , \left \lvert { \mathrm {Z+}}\right \rangle \}$ or X basis. (b) Transceiver microscopic picture with indicated circuit. TX: transmitter; RX: receiver. Test areas are marked in grey. The first MZI after the TX input serves as an optional on-chip optical attenuator. TOMs have a consistent $P_{\pi }$ of 26 mW, corresponding to a $V_{\pi }$ around 11 V. High-speed CDM structures are used in the traveling wave modulator with on-chip terminations. A $V_{\pi /2}$ of 9 V is observed in all structures. The length difference between the two arms of the AMZI is 7.9 mm, resulting in a 960 ps delay between two time-bins. Multi-mode waveguides are used in the delay line to reduce the average propagation loss to 1.25 dB/cm. Stable optical inputs/outputs are achieved with a fiber-array aligned to low-loss (2.4 dB per port) grating couplers.
Fig. 2. Schematic of the QKD test setup: Red solid lines with arrow represent the direction of the laser. Black dashed lines represent electrical connection or information flows. Polarization states in all the fiber channel are well controlled to maintain a best coupling efficiency. SiP: silicon photonic, Pol. C.: polarization controller, Ph. Rnd.: phase randomizer.
2.2 Feedback implementation
The degradation of the QBER of X basis is mainly caused by the cumulative phase shift in the delay line of the AMZI when the effective refractive index of the waveguide changes with the chip temperature, resulting in a shift of the static working point. Given the structure of the waveguide (Si strips of 450 nm (single mode) and 3 µm (multimode) in width cladded with $\mathrm {SiO}_2$), the effective thermal-optic coefficient can be simulated using the finite element method: $\mathrm {d}n_{\mathrm {eff}}/\mathrm {d}T\approx$ 2.02×10−4 K−1 [26,30]. Therefore, the cumulative phase-shift-temperature dependence in our transceiver is as high as $\mathrm {d}\theta /\mathrm {d}T=2\pi \Delta L\left (\mathrm {d}n_\mathrm {eff}/\mathrm {d}T\right )/\lambda \approx$ 65.26 rad K−1, in which $\Delta L=7.97$ cm is the delay line length and $\lambda =1550$ nm is the wavelength. Thus, a $\pi$ phase shift will occur when the temperature change is only 0.048 $^{\circ }$C, set aside that the temperatures of the transmitter and the receiver may vary independently. Meanwhile, no significant influence of the temperature on the performance of a MZI is detected, proving its symmetric geometry. Nevertheless, we still observed small drifts (within 1 V for voltages on TOM) of the static working point of Z basis during the whole period of test, which may be due to some unknown mechanisms that are related to the highly doped Si heaters.
To tackle these problems, we designed and implemented a feedback program for properly initializing and stabilizing the static working point for both bases. The photon state at the static working point at the outputs of the receiver (before the detector) is described by Eq. (1):
Fig. 3. Histogram of photon counts from the two outputs of the receiver under individual state preparation and measurement tests. According to the temporal position of the detection event, Bob passively select to measure in Z or X basis and distinguish the two eigenstates of Z basis. With the aid of spatial information of the interferencing maximum, Bob is able to discriminate the two eigenstates of X basis. Any basis-selection mismatches will lead to irrelevant results between Alice and Bob. Probability amplitude in Eq. (1) can be evaluated separately from time windows indicated by dash lines.
Four parameters (Eqs. (2)–(5)) calculated from a small amount of exchanged sifted keys are employed to minimize the average QBER within a few steps:
- (i) $\mathrm {QBER}_{\mathrm {Z}}$: When the $V_{\pi /2}$ on the CDMs is accurately applied, $\mathrm {QBER}_{\mathrm {Z}}$ is only related to $\Delta \theta _{\mathrm {a3}}$. An extrapolated relation is used to calculate the adjustment amount of the power applied on the TOM according to the current $\mathrm {QBER}_{\mathrm {Z}}$ value if it exceeds a threshold. However, due to the cosine nature of this relation, the proper adjustment can be either negative or positive. Therefore, up to two attempts may be made to determine this direction.
- (ii) $B_{\mathrm {Z}}$ and $B_{\mathrm {X}}$: $B_{\mathrm {Z(X)}}$ are used to evaluate if the loss of two arms of AMZI-b2(a2) are balanced, i.e., the minimum should be reached when the TOMs of MZI-b1(a1)is set at $\Delta \theta _{\mathrm {b(a)}}=2\arctan {\sqrt {\alpha _{\mathrm {bs(as)}}/\alpha _{\mathrm {bl(al)}}}}$ if the previous adjustment is done properly. $B_{\mathrm {Z}}$ should be adjusted before $B_{\mathrm {X}}$. The relation between $B_{\mathrm {Z(X)}}$ and the power applied on the TOMs in MZI-b1(a1) is approximated as linear around $B_{\mathrm {Z(X)}}=0$.
- (iii) $\mathrm {QBER}_{\mathrm {X}}$: The interference visibility of photons in the middle time-bin can reach to $>99\%$ when the first three parameters are optimized. Therefore, the $\mathrm {QBER}_{\mathrm {X}}$ has a simple cosine relation with the powers applied on the TOM in AMZI-a and AMZI-b. Similarly, the direction of the adjustment needs to be decided with up to two attempts.
2.3 Results
We demonstrated the QKD based on our silicon photonic transceiver using the decoy-state scheme. Three kinds of pulses, namely, signal, decoy and vacuum, with average photon number of 0.8, 0.07 and ${1 \times {10}^{-3}}$ were pseudo-randomly generated on chip with probability of 0.93, 0.06 and 0.01, respectively. Those values are optimized for a theoretically maximum secure key rate for a 20 km transmission in fiber. Another parameter needed to be carefully determined is the temporal width of the window in which Bob chooses to detect signals. Due to the Gaussian span of the pulses in time, a bigger window covers more real detection signals, as well as more dark counts that leads to a higher QBER. Such effect is more significant for long transmission distances, as an example shown in Fig. 4(a). To first evaluate the highest secure key rate which our system can achieve, tests were perform under stable chip temperatures (corresponding to the reference frame misalignment slower than 0.25$\pi$/min). By assuming a continuous phase randomization, as well as the condition of asymptotic regime of infinitely long keys and a non-ideal error correct function $f=1.2$ [31], we estimate the secure key rates at different transmission distances based on the raw data and QBER results, as shown in Fig. 4(b). A secure key rate of 85.7 kbps is expected over a 20 km fiber with a measured average QBER of 0.84%. It is worth noting that these key rates are the upper bounds and a more accurate analysis is necessary if the characteristics of the final system and a finite size of exchanged keys are considered [32,33].
Fig. 4. Estimated secure key rate: (a) Measured average QBER at different transmission distance. A 200 ps detection window is used. Inset: relation between the temporal width of the detection window and the secure key rate at 110 km (horizontal axis: window width in ps; vertical axis: secure key rate in bit per pulse); (b) Secure key rate calculated based on the measured raw data rate and QBER using the method from [31]. Transmission distance is emulated using an optical attenuator assuming a standard fiber loss: 0.2 dB/km.
The normal QKD operations is interleaved with the feedback procedures which collects and analyzes a fixed amount of raw data (6 kb). To test the feasibility of our feedback method, QKD under varying chip temperatures were performed with the feedback function being turned off and on. As shown in Fig. 5(a), when the temperature difference ($\Delta T$) between the transmitter and the receiver rises by 3 $^{\circ }$C, $\mathrm {QBER}_{\mathrm {X}}$ undergoes a few rounds of oscillation between 0 and 100%. A $\pi$ phase shift of $\Delta \theta _{\mathrm {a2}}-\Delta \theta _{\mathrm {b2}}$ indicated in Fig. 5(a) corresponds to a rise in temperature of 0.0471 $^{\circ }$C, which agrees with our previous estimation. On the contrary, the $\mathrm {QBER}_{\mathrm {Z}}$ shows great robustness as predicted. Under a similar condition, the feedback function significantly improves the performance by achieving in an average $\mathrm {QBER}_{\mathrm {X}}$ of 4.4% and a total QBER of 2.6% in the first 30 min of the test, as shown in Fig. 5(b). The following 1.5 hour operation in a varying room temperature shown in the inset of Fig. 5(b) proves the stabilization of the system.
Fig. 5. Comparison of QBER with the feedback function turned (a) off and (b) on as the temperature difference between the transmitter and receiver ($\Delta T$) increases. The range indicated by a pair of arrows in (a) corresponds to a $\pi$ phase shift of $\Delta \theta _{\mathrm {a2}}-\Delta \theta _{\mathrm {b2}}$. Occasional peaks of $\mathrm {QBER}_{\mathrm {X}}$ in (b) is due to the wrong adjustment direction and can be corrected immediately. Inset of (a): Temperature changes are realized by opposite relaxations of transmitter and receiver from a specific temperature controlled by thermoelectric cooling setups (horizontal axis: time in min; vertical axis: temperature in $^{\circ }$C). Inset of (b): long-time operation test in room temperature (axes and legends are same as (b)).
To provide a quantitative analysis of the correction ability of the feedback function, we plot the $\mathrm {QBER}_{\mathrm {Z}}$ and $\mathrm {QBER}_{\mathrm {X}}$ as a function of the changing rate of $\Delta T$ (Fig. 6(a)). Obviously lower $\mathrm {QBER}_{\mathrm {X}}$s are observed when the changing rate is smaller than 0.2 $^{\circ }$C/min (corresponding to the reference frame misalignment slower than 4$\pi$/min). We believe that the feedback functionality is closely related to the frequency of sampling and correcting the parameters, as shown in a comparison between Figs. 6(a) and 6(b). Due to our limited hardware resources, the system requires at least 1 s to communicate and analyze a considerable amount of raw data (6 kb in the cases shown in Fig. 6). Future improvements to increase the sampling frequency may include the utilization of a specific feedback module integrated with time-to-digital conversion functions, which can be realized by a field-programmable-gate-array (FPGA). Meanwhile, from practical perspectives, high-frequency part of the temperature fluctuation can be suppressed by some heat isolation and buffering approaches.
Fig. 6. Comparison of correction abilities of the feedback function under sampling frequencies of (a) 1 Hz and (b) 0.2 Hz. In both cases, a same amount of raw data (6 kb) is collected and analyzed for every sampling point.
3. Conclusion
To achieve wider deployments of QKD, we envisage that various protocols and hardware forms may coexist to fulfill different application scenarios. With less single photon detectors and no active selection of basis on Bob side, time-bin protocol shows great advantage on reducing the cost and complexity of the QKD system. And such advantage can be extended by replacing bulky fiber systems with silicon photonic transceiver. In this article, a highly integrated silicon photonic QKD transceiver based on the time-bin protocol is demonstrated with an estimated secure key rate up to 85.7 kbps over 20 km fiber. With the help of an effective feedback method, a low QBER can be maintained under the fluctuation of temperatures of the two communicating devices for long-time operations. To provide a more robust system with higher key rates, further optimizations of the feedback function and a higher clock rate remain to be implemented to take full advantage of the high modulation bandwidth of the CDM [29]. Moreover, future improvements may also include fully integration of light sources with phase randomization or single photon avalanche diodes on chip [34,35]. In the field of QKD research and application, we believe this work paves the route towards truly simple and feasible QKD transceiver based on silicon photonics and inspires new forms of QKD deployment, such as portable QKD devices and seamless integrations with classical communication units.
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