Analysis of the Impact of Homodyne Detection Efficiency on Remote State Preparation

Resumo

Continuous-variable quantum key distribution (CV-QKD) is a leading technology for secure communication, whose security guarantees fundamentally rely on the quantum nature of the transmitted states and the measurement process. However, real-world detectors invariably suffer from limitations, such as inefficiency, which affects the overall security and performance of the system. Here, we investigate the impact of detector efficiency on remote state preparation in the context of entanglement-based CV-QKD. Specifically, by using the Wigner function formalism and starting from a two-mode squeezed vacuum state, we derive the analytical
form of the quantum state of one mode conditioned on a homodyne measurement performed on the other mode. Our analysis explicitly contrasts the ideal case of unit efficiency (η=1), which prepares a pure, displaced squeezed state, with the non-ideal scenario. For η < 1, we demonstrate that the preparation result is a mixed
state characterized by increased noise and degraded squeezing. We calculate the exact analytical expressions for the conditional state’s variance and mean displacement, quantifying their dependence on both the efficiency η and the initial squeezing parameter.