Evaluation of the phase randomness of the light source in quantum key   distribution systems with an attenuated laser
  The phase randomized light is one of the key assumptions in the security proof of Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol implemented with an attenuated laser. Though the assumption has been believed to be satisfied for conventional systems, it should be reexamined for current high speed QKD systems. The phase correlation may be induced by the overlap of the optical pulses, the interval of which decreases as the clock frequency. The phase randomness was investigated experimentally by measuring the visibility of interference. An asymmetric Mach-Zehnder interferometer was used to observe the interference between adjacent pulses from a gain-switched distributed feedback laser diode driven at 10 GHz. Low visibility was observed when the minimum drive current was set far below the threshold, while the interference emerged when the minimum drive current was close to the threshold. Theoretical evaluation on the impact of the imperfect phase randomization provides target values for the visibility to guarantee the phase randomness. The experimental and theoretical results show that secure implementation of decoy BB84 protocol is achievable even for the 10-GHz clock frequency, by using the laser diode under proper operating conditions. 
Toshiya Kobayashi, Akihisa Tomita, and Atsushi Okamoto
quant-ph