Spoofing resilience for simple-detection quantum illumination LIDAR

TL;DR

The paper tackles spoofing resilience in a simple-detection quantum-illumination LIDAR framework by modeling an intruder with real/false channels and a basis-biasing strategy. It introduces the $k$-factor security metric $k=\frac{\mathrm{Pr}^{\mathfrak{E}}_\mathrm{c}-\mathrm{Pr}^{\mathrm{B}}_\mathrm{c}}{\mathrm{Pr}^{\mathfrak{E}}_\mathrm{w}-\mathrm{Pr}^{\mathrm{B}}_\mathrm{w}}$ and the associated Eve error $e_\mathfrak{E}=\frac{1}{k+1}$, along with an offset threshold $e_{\mathrm{T,off}}$ to cope with incomplete intrusion and limited sampling. The work demonstrates that Eve can sometimes minimize induced error by selecting an optimal relative basis angle $\theta$, but that spoofing resilience can be achieved through parameter-aware verification and discrepancy-based recognition, even with limited samples via Skellam-based distributions. Compared to BB84-inspired classical imaging, QI exhibits superior SNR in weak-signal/high-noise regimes and provides a practical framework for intrusion recognition and trustworthy return-signal extraction in active remote sensing. The results have practical implications for secure, noise-robust quantum sensing and suggest directions for extending multi-basis encoding and underwater scenarios.

Abstract

Object detection and range finding using a weak light source is vulnerable to jamming and spoofing attacks by an intruder. Quantum illumination with nonsimultaneous, phase-insensitive coincidence measurements can provide jamming resilience compared to identical measurements for classical illumination. We extend an experimentally-feasible object detection and range finding quantum illumination-based protocol to include spoofing resilience. This approach allows the system to be characterised by its experimental parameters and quantum states, rather than just its detector data. Therefore we can scope the parameter-space which provides some spoofing resilience without relying upon the prohibitive method of acquiring detector data for all combinations of the experimental parameters. We demonstrate that in certain regimes the intruder has an optimal relative detection basis angle to minimise the induced error. We also show that there are spoofing-vulnerable regimes where excessive background noise prevents any induced error, while it is still possible to perform object detection, i.e. our detectors have not been fully blinded. The sensing protocol which we describe can allow for the recognition of intrusion and the possible detection of our trustworthy return signal. Our results reinforce that quantum illumination is advantageous for spoofing resilience compared to a classical illumination-based protocol.

Figures (9)

• Figure 1: Beamsplitter diagram of the intrusion of Eve upon Alice's signal mode light, if Alice measures in the H/V basis and Eve measures in her $\tilde{\mathrm{h}}/\tilde{\mathrm{v}}$ basis. This figure visualises the beamsplitter model which we use to calculate the click probabilities for the idler detectors $\mathrm{Pr}_\mathrm{I:\mathcal{X}_+}$ and the click probabilities for Eve's detectors $\mathrm{Pr}_{\mathrm{S:\mathcal{Y}_+\vert I:\mathcal{X}_+}}(\theta_\mathrm{T})$. The beamsplitter transmission parameter relevant to Alice's idler detectors or Eve's signal detectors is set by the corresponding detector quantum efficiency $\eta_{\mathrm{I}/\mathfrak{E}}$.
• Figure 2: Beamsplitter diagram of Alice's H/V signal detectors when Eve's light is incident. This choice of basis is predetermined from Alice's idler detector system not pictured. In this figure, the click probabilities for Alice's signal detectors relates to $\mathrm{Pr}_\mathrm{S:\mathcal{Z}_+\vert E:\mathcal{Y}}(\theta_\mathrm{T})$. Here, the beamsplitter transmission parameter relevant to Alice's signal detectors is the product of the detector quantum efficiency $\eta$ and signal attenuation (set by Eve) $\xi_\mathfrak{E}$.
• Figure 3: Visual comparison of Alice's MUB to the MUB of Eve, for a relative basis angle $0<\theta<\frac{\pi}{4}$.
• Figure 4: The error rate of Eve's (isolated) contribution to Alice's detection statistics as a function of relative basis angle $\theta$. For the parameter regime detailed in Appendix \ref{['appendix:parameters']} there is a minimal error for a particular relative basis angle $\theta$. The quantum efficiencies of Eve's and Alice's signal detectors are all different, which causes the variation of the error rate shown.
• Figure 5: SNR for the real and false channels as a function of probability of interception $p$. The parameter regime is detailed in Appendix \ref{['appendix:parameters']}.