Security formulas of QKD with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector.

The asymptotic key generation (AKG) rates with the decoy method are discussed in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of intensities. For this purpose, we derive a useful convex expansion of the phase-randomized coherent state. We also derive upper bounds of AKG rates on a natural and concrete channel model. Using these upper bounds, we numerically check that the AKG rates are almost saturated when the number of intensities is three.

Further, applying the above results, we evaluated the security of implementable QKD system by the decoy method.


References:

• 1) M. Hayashi, "Upper bounds of eavesdropper's performances in finite-length code with the decoy method", Physical Review A 76, 012329 (2007)
• 2) M. Hayashi, "General theory for decoy-state quantum key distribution with an arbitrary number of intensities", New J. Phys. 9, 284 (2007)
• 3) Jun Hasegawa, Masahito Hayashi, Tohya Hiroshima, Akihisa Tomita, "Security analysis of decoy state quantum key distribution incorporating finite statistics", arXiv:0707.3541
• 4) Jun Hasegawa, Masahito Hayashi, Tohya Hiroshima, Akihiro Tanaka, Akihisa Tomita, "Experimental Decoy State Quantum Key Distribution with Unconditional Security Incorporating Finite Statistics", arXiv:0705.3081

Seminar, 15th of November, 15:00h. Conference Room

Hosted by Prof. Antonio Acín