Imperfect detectors for adversarial tasks with applications to quantum key distribution

Security analyses in quantum key distribution (QKD) and other adversarial quantum tasks often assume perfect device models. However, real-world implementations often deviate from these models. Thus, it is important to develop security proofs that account for such deviations from ideality. In this work, we extend the idea of squashing maps to develop a general framework for analysing imperfect threshold detectors, treating uncharacterised device parameters such as dark counts and detection efficiencies as adversarially controlled within some ranges. This approach enables a rigorous worst-case analysis with exactly characterised devices, ensuring security proofs remain valid under realistic conditions. Our results strengthen the connection between theoretical security and practical implementations by introducing a flexible framework for integrating detector imperfections into adversarial quantum protocols.