  In 2005, trace distance between an ideal quantum state to be distributed and
an actual quantum state distributed was introduced as a valid security measure
of Quantum Key Distribution (QKD) by R. Renner et al., then it has been
perceived that the trace can be interpreted as a maximum failure probability of
QKD. While such a perspective has been widely accepted, H. P. Yuen and O.
Hirota have been warning that such an interpretation is not correct since 2009.
The author of this study has been giving questions on the interpretation of the
trace distance based on their criticisms since QIT30 in May 2014, and has been
proposing Yuen's idea to evaluate the security of QKD by the probability for
the attacker to guess the correct key. However, the author could not give the
guessing probability concretely. In this study, the author explains how to
derive the average guessing probability for the attacker, where its result
equals to Yuen's derivation firstly seen in 2010. From this result, one will
see the problems with the maximum failure probability interpretation of the
trace distance clearly. This study also explains the indistinguishability
advantage interpretation is also invalid.
