Hacking continuous-variable quantum key distribution using the photorefractive effect on proton-exchanged/annealed-proton-exchanged waveguide

Lithium niobate materials, which have the potential to fabricate lasers, modulation devices, and photodetectors, are widely used in quantum information processing due to their exceptional optical and electro-optical properties. However, the photorefractive effect in lithium niobate materials may cause the quantum device to deviate from its ideal operation model, which is an important assumption for the security of quantum key distribution. Here, we demonstrate the practical security of the continuous-variable quantum key distribution protocol under the photorefractive effect, where the eavesdropper Eve injects a 488 nm visible light into the source-side variable optical attenuator and excites the photorefractive effect phenomenon in a lithium-niobate-based dual-waveguide. In particular, we derive the photorefractive-effect-induced intensity change of a variable optical attenuator and then the corresponding parameter estimation process, showing the effectiveness of this attack for various irradiation powers and waveguide technologies (including proton-exchanged and annealed-proton-exchanged waveguides). To show its effect on practical continuous-variable quantum key distribution systems, we present the composable finite-size security of one-way continuous-variable quantum key distribution and continuous-variable measurement-device-independent quantum key distribution protocols. Numerical results show that this induced-photorefraction attack can break the security even with a low irradiation power, such as 3 [Formula: see text] (or about 0.21 [Formula: see text]). In addition, we find that Eve's optimal attack strategy against continuous-variable measurement-device-independent quantum key distribution is related to the information reconciliation process by comparing three different attack strategies. Finally, we discuss some possible countermeasures to resist induced-photorefraction attacks to enhance the security of the system.