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Optics Express

Phase noise estimation using Bayesian inference for continuous-variable quantum key distribution

Wei Zhao, Ying Guo, Ling Zhang, Duan Huang

Published Jan 22, 2019• 10 citations
Publisher

Abstract

Excess noise induced by the phase drifts is a serious impairment for the continuous-variable quantum key distribution with locally generated local oscillator scheme, which is recently proposed to avoid the side channel attacks due to the transmitted local oscillator. Theoretical and experimental studies on the phase estimation have been widely reported, while two frequency-locked laser sources are indispensable to achieve quantum coherent detection. Moreover, the self-referenced phase estimation scheme requires to propagate the strong reference pulse through optical fiber, which opens a security loophole through the manipulation of the reference pulse amplitude. Based on the theoretical security and Bayes' theorem, we propose a phase estimation protocol, which does not require propagating the strong reference pulse for performing phase estimation. Compared to the other related work, the protocol can avoid the security problem caused by strong reference pulse. Moreover, this algorithm is an iterative progress for each of experiment to obtain the phase estimation and its uncertainty. We hope the proposed scheme could further promote the performance of continuous-variable quantum key distribution.

DOI
10.1364/oe.27.001838

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Excess noise induced by the phase drifts is a serious impairment for the continuous-variable quantum key distribution with locally generated local oscillator scheme, which is recently proposed to avoid the side channel attacks due to the transmitted local oscillator. Theoretical and experimental studies on the phase estimation have been widely reported, while two frequency-locked laser sources are indispensable to achieve quantum coherent detection. Moreover, the self-referenced phase estimation scheme requires to propagate the strong reference pulse through optical fiber, which opens a security loophole through the manipulation of the reference pulse amplitude. Based on the theoretical security and Bayes' theorem, we propose a phase estimation protocol, which does not require propagating the strong reference pulse for performing phase estimation. Compared to the other related work, the protocol can avoid the security problem caused by strong reference pulse. Moreover, this algorithm is an iterative progress for each of experiment to obtain the phase estimation and its uncertainty. We hope the proposed scheme could further promote the performance of continuous-variable quantum key distribution.
Measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD) protocol calibrates the phase reference frames by transmitting local oscillator pulses between two legitimate parties. The above implementation leaves massive loopholes; in particular, an eavesdropper can attack the system by manipulating the power of the local oscillator pulses. In this paper, a Bayesian phase-noise estimation model is proposed to estimate the phase drift and its uncertainty in the MDI-CVQKD protocol. The model employs the Bayesian estimation of the very weak quantum signal pulses and eliminates the necessity of transmitting local oscillator pulses between two legitimate parties. Moreover, the Bayesian inference algorithm has the characteristic of high robustness to noise and can achieve a well-motivated confidence interval of the estimated eigenphase. Comparing with its Gaussian counterpart, we adopt the discrete modulation in the MDI-CVQKD protocol, which allows a much better reconciliation efficiency at low signal-to-noise ratio. With simpler implementation, the proposed Bayesian phase-noise estimation model precisely avoids the security bottleneck due to the transmitted local oscillator pulses.
In practical continuous-variable quantum key distribution system using local local oscillator (LLO CV-QKD), the phase noise related to coherent detection and phase-reference pulse intensity that can be locally calibrated at the receiver side is considered to be trusted noise to improve the performance. However, if the intensity of the phase-reference pulse is not monitored precisely in real-time, a security loophole will be opened for the eavesdropper to launch attacks. To this end, we propose two practical phase-reference pulse intensity attack strategies, where Eve can reduce the trusted phase noise by manipulating the intensity of the phase-reference pulse, thereby hiding her attack on the signal pulse if the total excess noise remains unchanged. The performance of the LLO CV-QKD system under these attacks has been analyzed. We show that precisely monitoring the intensity of the phase-reference pulse in real-time is an essential countermeasure to prevent the proposed attacks. Moreover, an intensity-monitoring scheme for the phase-reference pulse is proposed to strengthen the security of the practical LLO CV-QKD system and make the trusted phase noise model more robust.
We study the validity of partially trusting the phase noise associated with estimation uncertainty in a continuous variable quantum key distribution system with a local local oscillator (LLO-CVQKD) and investigate optimal system parameters. We find that the trusted phase noise model enhances the key rate and transmission distance performance but opens a security loophole by manipulating the reference pulse amplitude. Therefore, we propose a “reference pulse attack” on the trusted phase noise LLO-CVQKD system where Eve achieves 100% information hacking without being detected at 23.8km and 32.0km while using lossless and 0.14dB/km loss channels, respectively. Nevertheless, by re-analyzing the attack, countermeasures are also proposed to keep the performance advantages of the trusted phase noise model. As a result, the trusted phase noise LLO-CVQKD can still provide a superior secure key rate (e.g., 9 times higher key rate at 20km) and an increased transmission distance by 45%, compared to that of the untrusted phase noise system.
By manipulating the reference pulses amplitude, a security vulnerability is caused by self-reference continuous-variable quantum key distribution. In this paper, we formalize an attack strategy for reference pulses, showing that the proposed attack can compromise the practical security of CVQKD protocol. In this scheme, before the beam splitter attack, Eve intercepts the reference pulses emitted by Alice, using Bayesian algorithm to estimate phase shifts. Subsequently, other reference pulses are re-prepared and resubmitted to Bob. In simulations, Bayesian algorithm effectively estimates the phase drifts and has the high robustness to noise. Therefore, the eavesdropper can bias the excess noise due to the intercept-resend attack and the beam splitter attack. And Alice and Bob believe that their excess noise is below the null key threshold and can still share a secret key. Consequently, the proposed attack shows that its practical security can be compromised by transmitting the reference pulses in the continuous-variable quantum key distribution protocol.
Continuous-variable quantum key distribution (CVQKD) with a real local oscillator (LO) is confronted with new security issues attributed to the reference pulses transmitted together with quantum signals over the insecure quantum channel. This paper proposes a method of phase attack on reference pulses of the CVQKD with real LOs. Under the phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers so that the phase compensation error is increased. Consequently, the secret key rate is reduced because of the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, both the parameters of actual transmittance and actual excess noise are deduced from the phase compensation accuracy, and then they are compared with those estimated by training signals. The simulation results show that the secret key rate calculated from the theoretical parameters is consistent with the one estimated by training signals.
The continuous-variable quantum key distribution with a local local-oscillator is extremely sensitive to the phase compensation noise caused by the inaccurate reference phase estimation. In order to overcome the influence of slow drift caused by the residual optical frequency difference, we utilize a vector Kalman filter to estimate and track the reference phase from pilots. The fast drift and slow drift are taken into account in the variation of the reference phase, so that phase estimation becomes more accurate than the conventional scalar Kalman filter. The mean square error of reference phase estimation is deduced theoretically, and the specified frame is designed to estimate the phase noise variance in real time. In simulations, the performances involving of the estimation accuracy, the actual excess noise and the secret key rate are compared between with four different phase estimation methods. The simulation results show that the vector Kalman filter is superior to the other methods, even though under a serious phase noise and a large optical frequency difference.