Entanglement-based continuous-variable quantum key distribution with multimode states and detectors

Secure quantum key distribution with multimode Gaussian entangled states and multimode homodyne detectors is proposed. In general the multimode character of both the sources of entanglement and the homodyne detectors can cause a security break even for a perfect channel when trusted parties are unaware of the detection structure. Taking into account the multimode structure and potential leakage of information from a homodyne detector reduces the loss of security to some extent. We suggest the symmetrization of the multimode sources of entanglement as an efficient method allowing us to fully recover the security irrespectively to multimode structure of the homodyne detectors. Further, we demonstrate that by increasing the number of the fluctuating but similar source modes the multimode protocol stabilizes the security of the quantum key distribution. The result opens the pathway towards quantum key distribution with multimode sources and detectors.