  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.

Quantum Physics