Securing Practical Quantum Communication Systems with Optical Power Limiters

Controlling the energy of unauthorized light signals in a quantum cryptosystem is an essential criterion for implementation security. Here, we propose a passive optical power limiter device based on thermo-optical defocusing effects, providing a reliable power limiting threshold that can be readily adjusted to suit various quantum applications. In addition, the device is robust against a wide variety of signal variations (e.g., wavelength, pulse width), which is important for implementation security. We experimentally show that the proposed device does not compromise quantum communication signals. It only has a minimal impact (if not, negligible impact) on the intensity, phase, or polarization degrees of freedom of the photons, thus making it suitable for general communication purposes. To show its practical utility for quantum cryptography, we demonstrate and discuss three potential applications: (1) measurement-device-independent quantum key distribution with enhanced security against a general class of Trojan-horse attacks, (2) using the power limiter as a countermeasure against bright illumination attacks, and (3) the application of power limiters to potentially enhance the implementation security of plug-and-play quantum key distribution.

Popular Summary

The implementation of quantum cryptography typically requires that both the involved optical devices and quantum signals are operating in the single-photon regime. This assumption is needed to ensure that quantum principles such as the no-cloning and Heisenberg uncertainty principles are in effect. In the recent decade, however, applied research has shown that this assumption is very difficult to enforce in practice as the attacker can easily inject bright light pulses into the communication system to invalidate the underlying quantum principles. This method has since formed the basis for most of today’s quantum hacking techniques like the Trojan-horse attacks and detector blinding attacks.

To harden the implementation security of quantum communications against such attacks, we propose a passive device called the “quantum optical power limiter,” which effectively blocks the optical communication whenever the energy level is above some tolerated threshold. We show that the proposed optical power limiter is highly compatible with popular quantum communication encoding schemes like time-bin, phase, and polarization encodings, and that it introduces almost zero noise to the quantum bit error rate. We also provide a security analysis that takes into account the energy constraint imposed by the optical power limiter and show that it can significantly strengthen the security of practical quantum key distribution. Based on the broad utility of the proposed quantum optical power limiter, we believe that it could also find applications in secure distributed quantum blind computing and other quantum communication tasks.

Figure 1

Schematic of the power limiter design. An acrylic prism is used as the active medium. When the absorbed energy introduces temperature gradients inside the prism, the input collimated Gaussian beam diverges due to the thermo-optical defocusing effect. A diaphragm is placed after the prism to control the collectible optical power. The optical filter restricts the working wavelength range for security analysis. The inset is the top view of the acrylic prism and the diverged Gaussian beam. Owing to the isotropic nature of acrylic, both the optical and thermal responses are assumed to be axially symmetric along the optical axis.

Figure 2

Simulated (a) temperature and (b) $E$-field distribution in the region marked with the dashed box in Fig. 1 using a two-dimensional model in comsol. The results clearly indicate the high-temperature gradient in the $r$ direction and the gradual divergence of the Gaussian profile in the $r$ direction. Simulated (c) maximum output power and (d) insertion loss at different diaphragm widths and prism lengths using Eq. (2), where $\alpha =25.95{\mathrm{m}}^{-1}$ (measured value), $\mathrm{TOC}=-1.3\times {10}^{-4}{\mathrm{K}}^{-1}$ [58], $n=1.47$ [29], $k=0.19{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ [30], $a=140\mu \mathrm{m}$. (e) Experimental output-input power relationship at different diaphragm widths with the same prism length of 101.6 mm. The results indicate that the smaller the diaphragm width, the lower the output power threshold. Also, with a diaphragm width larger than the beam width, the insertion loss remains minimum. (f) Experimental output-input power relationship at different prism lengths but with the same diaphragm width of $25\mu \mathrm{m}$. Longer prism lengths could provide a lower output power threshold, but the insertion loss could be higher. Both the simulation and experimental results confirm the power limiting effect of our design, and an adjustable power limiting threshold is feasible.

Figure 3

(a) Experimental output response of the power limiter at different input optical powers. A 101.6 mm prism is used with a $750\mu \mathrm{m}$ diaphragm. The power limiting effect has a long settling time of around 300 ms. (b) Experimental output response of the power limiter with constant-energy pulse input. A 101.6 mm prism is used with a $25\mu \mathrm{m}$ diaphragm. The peak power and duty cycle are selected to maintain the same energy per pulse or the same average input power of 10.5 dBm. (c) The average output power at different duty cycles with average input powers of 10.5 and 13 dBm shows that the maximum output power occurs at a duty cycle of 1, i.e., CW input. (d) The comsol simulated maximum temperature inside the prism with constant pulse energy of 97.8 mJ and pulse widths of about 0.5 to 13.5 s, which correspond to an average input power of 9.78 mW in a 10 s time span. The result shows that higher peak power heats the prism faster and reaches a higher temperature. Thus, a higher thermo-optical effect can be expected.

Figure 4

(a) Calculated $f[n(\lambda )]$ from Eq. (3) and the output power threshold difference caused by the corresponding TOC change, as referenced to the value at 1550 nm. (b) Absorption loss spectrum of acrylic, taken from Refs. [29, 34]. The losses at the 1310 and 1550 nm communication bands are marked. The minimum loss is about 0.15 dB/cm at visible wavelength. (c) The maximum output power of the power limiter and the corresponding input power with silicon absorber (visible light absorbing filter) of different lengths. The silicon absorber significantly reduces the power threshold at the visible wavelength. (d) The total maximum output photon number per second calculated from (c) a the silicon absorber thickness of 1 mm.

Figure 5

(a),(b) The number of counts as a function of the delay between the APD gate and laser pulse in the intensity encoding scheme. The results with and without power limiter (PL) are shown. (a) The case for 14.49 dBm input power, which is close to the power limiting threshold. (b) The case for $-19.72$ dBm input power. The discontinuity of the curve is because of the negative count values obtained due to the statistical noise. (c) Experimental setup for the QBER measurement of the phase encoding scheme. The input CW light is modulated with a phase modulator switching between 0 and $\pi$ phases and decoded with an AMZI, which generates a constructive or a destructive interference output, marked as max and min, respectively. The peaks at about 0 and 10 ns are caused by the AMZI path inaccuracy. The output light is attenuated to the single-photon level and measured with an APD. (d),(e) The count value with minimum and maximum phase shifter settings as a function of the delay between the APD gate and the phase modulator clock in the phase encoding scheme. (f) The calculated interference visibility as a function of the delay between the APD gate and the phase modulator clock with and without the power limiter in the phase encoding scheme. (g) Experimental setup for the QBER measurement of the polarization encoding scheme. The polarization of an attenuated CW laser is manually tuned to match the polarization of a polarization beam splitter (PBS). The output from the PBS is measured by two APDs.

Figure 6

Schematic of the phase-encoding MDI-QKD [37] system with the power limiter installed. For each round, using their lasers, modulators, and attenuators, Alice and Bob prepare one of the four coherent states $\{|\alpha e^{ix\pi /2}⟩{\}}_x$ and $\{|\beta e^{iy\pi /2}⟩{\}}_y$, where $x,y\in \{0,1,2,3\}$. They would then send their respective quantum states to Charlie for Bell-state measurement, who would then announce the outcome of his measurement $z\in \{L,R,\varnothing \}$. If Charlie announces $z=\varnothing$, they would discard the data for that round; otherwise, they would keep their respective choices $x$ and $y$. After many rounds, they perform sifting and parameter estimation, and if they do not abort the protocol, they will also perform error correction and privacy amplification to extract identical and secret keys. Based on the power limiting threshold, the Trojan-horse attack from Eve could provide her with an average of $\nu$ Trojan-horse photons per pulse, which is taken into consideration for secure key rate calculation.

Figure 7

Simulation of the asymptotic key rate for phase-encoding MDI QKD under two sets of parameters: (a) detector’s efficiency ${\eta }_{\det }=10\mathrm{\%}$, dark count rate $p_{\mathrm{dc}}={10}^{-5}$, (b) detector’s efficiency ${\eta }_{\det }=85\mathrm{\%}$, dark count rate $p_{\mathrm{dc}}={10}^{-7}$. Trojan-horse photon numbers of $\nu ={10}^{-5}$, ${10}^{-6}$, ${10}^{-7}$ and 0 are shown. The output intensity $\mu$ of each transmitter is optimized for each distance to maximize the key rate.

Figure 8

(a) A schematic of the detector blinding attack proposed in Ref. [43]. (b) The current-voltage relationship of a typical APD. In normal working conditions, the breakdown voltage is $V_{\mathrm{Br}0}$. A fixed bias voltage $V_{\mathrm{Bias}}>V_{\mathrm{Br}0}$ enables Geiger mode operation with single-photon sensitivity. The resulting output current above a threshold $I_{\mathrm{Th}}$ is registered as a successful count. However, the breakdown voltage increases with the temperature $T$ of the device. Thus, it is possible to blind the detector by driving it into the linear mode ($V_{\mathrm{Bias}}<V_{\mathrm{Br}1}$), thus nullifying the single-photon sensitivity. (c) The current-input power relationship of an APD operating in linear mode. By controlling the input power below or above the power threshold $P_{\mathrm{Th}}$, the detector could be controlled to register fake states. (d) The input power on Bob’s detector with and without a power limiter.

Figure 9

Schematics of the power limiter used in (a) a plug-and-play MDI-QKD system and (b) a plug-and-play BB84 QKD system.