  Quantum Key Distribution (QKD) has been attracting researchers that it would
provide provable security to distribute secret keys since its birth in 1984.
Since 2005, the trace distance between an ideal quantum state and an actually
distributed state has been employed to evaluate its security level, and the
trace distance was given an interpretation that it would be a maximum failure
probability in distributing perfectly secure keys. However, in 2009, H. P. Yuen
criticized that the trace distance would not have such an interpretation. Since
then, O. Hirota, K. Kato, and T. Iwakoshi have been warning to make people pay
attention to Yuen's criticisms. In 2015, T. Iwakoshi precisely explained why
Yuen has been correct. In 2016, Yuen himself published a paper to explain the
potentially unsolved problems in QKD. This study precisely explains the most
important problems given in Yuen's paper, and gives recent topics around QKD
and other quantum cryptographic protocols.
