Detector noise in continuous-variable quantum key distribution

TL;DR

This work addresses the challenge of modeling detector noise in continuous-variable QKD by introducing a calibrated detector-noise model that assumes detector isolation but allows Eve to predict, not control, detector noise. The authors validate the approach with experimental measurements of a commercial homodyne detector and quantify the impact on the GMCS QKD secret-key rate, showing that when the detector-noise variance $\nu_B$ is well below vacuum noise, the calibrated model achieves rates close to the trusted-noise model. Numerical simulations across realistic detector-noise levels and channel losses indicate that the calibrated model significantly outperforms the untrusted-noise model while retaining practical performance and straightforward integration into existing CV-QKD setups. The work thus provides a physically plausible and implementable middle-ground that removes the hard requirement of truly random detector noise while preserving high key rates under typical operating conditions.

Abstract

In continuous-variable (CV) QKD with optical coherent detection, the widely adopted \textit{trusted detector noise} model improves both the secret key rate and the transmission distance. This model assumes that detector noise is inherently random and inaccessible to an adversary. While substantial research has focused on shielding the detector, it is far more difficult to justify the adversary's ignorance of the detector noise. In this paper, we introduce a \textit{calibrated detector noise} model for CV-QKD, which relies solely on the isolation of the detector from the adversary's intervention. Specifically, our model applies even when detector noise is predictable to the adversary. We analyze the electrical noise of a commercial balanced photoreceiver and perform numerical simulations to compare different noise models. Our results show that when the detector noise variance is an order of magnitude below the vacuum noise, the proposed model achieves a secret key rate comparable to that of the trusted detector noise model, while eliminating the questionable assumption of ``truly random'' detector noise.

Figures (5)

• Figure 1: Experimental setup. The local oscillator is attenuated to a desired power before entering a 50/50 beam-splitter with a vacuum state. The outputs then pass through manual attenuators before being measured by a balanced photoreceiver. The differential signal from the photoreceiver is sampled using a 200 MHz digital oscilloscope.
• Figure 2: Homodyne detection of a vacuum state at different local oscillator powers, with a detection bandwidth of 20 MHz (circular points) at gains of $5\times10^3$ V/A (blue) and $10\times10^3$ V/A (green), and a bandwidth of 500 MHz (square points) at gains of $5\times10^3$ V/A (red) and $10\times10^3$ V/A (purple). The dashed lines represent linear fits to the experimental data, with the corresponding fitting equations shown in the legend.
• Figure 3: Probability distributions of 5 million homodyne-detected samples acquired at $\mathrm{QCNR} = -\infty$ (blue) and $\mathrm{QCNR} = 5.5$ (orange). Small DC biases have been removed from the samples.
• Figure 4: Absolute values of autocorrelation (in log scale) of the homodyne output with $\mathrm{QCNR} = -\infty$ (blue) and $\mathrm{QCNR} = 5.5$ (orange). The dashed green line indicates the expected autocorrelation from a finite set of 5 million truly random numbers, at $\frac{1}{\sqrt{5,000,000}}\approx0.0005$.
• Figure 5: Key rates for GMCS QKD. The three different detector noise models are simulated: trusted (dashed line), untrusted (dash-dotted line), and calibrated (solid line). The electrical noises of the detector are $\nu_B=0.01$ (blue), $\nu_B=0.1$ (red), and $\nu_B=0.28$ (black). The zoom-in subplot shows the key rates in the low noise regime $\nu_B=0.01,0.1$, within the typical length of access networks (25km-50km). The key rates are optimized over the modulation variance $V_A$. Other simulation parameters are: $f=0.95$, $\eta_B=0.5$. The fiber attenuation used is $0.2$dB/km.