Optical modulation schemes for frequency-coded quantum key distribution

We discuss possible modulation schemes to implement BB84 and B92 quantum key distribution protocols using frequency-coding method. We derive time evolution of quantum states of light in a Mach-Zehnder interferometer based optical intensity modulator. We then show that phase modulator-phase modulator (PM-PM) combination can be used to implement the B92 protocol and intensity modulator-intensity modulator (IM-IM) combination can be used to implement the BB84 protocol. However, the combinations-PM-IM or IM-PM-cannot be used to implement BB84 and B92 protocols using frequency-coding method. Finally, we discuss the security of frequency-coded implementation of B92 protocol.