Single-photon continuous-variable quantum key distribution based on the energy-time uncertainty relation.

We propose a new quantum key distribution protocol in which information is encoded on continuous variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrowband single-photon pulse or the time delay of a broadband single-photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy-time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. Since no interferometer is employed in this scheme, it is more robust against various channel noises, such as polarization and phase fluctuations.