Practical Evaluation of Security for Quantum Key Distribution

Masahito Hayashi ∗ EARTO-SORST Quantum Computation and Information Project, JST 5-28-3, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan Superrobust Computation Project, Information Science and Technology Strategic Core (21st Century COE by MEXT) Graduate School of Information Science and Technology, The University of Tokyo 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan Abstract Many papers proved the security of quantum key distribution (QKD) system, in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system requires, it is needed to evaluate a protocol with a finite coding-length. For this purpose, we derive a tight upper bound of the eavesdropper’s information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper’s information. Further, we approximate our bound by using the normal distribution.