  We investigate the transition probabilities for the "flavor" eigenstates in
the two-level quantum system, which is described by a non-Hermitian Hamiltonian
with the parity and time-reversal (PT) symmetry. Particularly, we concentrate
on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian
Hamiltonian turn out to be a complex conjugate pair. In this case, we find that
the transition probabilities will be unbounded in the limit of infinite time $t
\to +\infty$. However, after performing a connection between a non-Hermitian
system, which exhibits passive PT-symmetry and global decay, and the
neutral-meson system in particle physics, we observe that the diverging
behavior of the transition probabilities is actually applicable to the
gauge-transformed neutral-meson states, whereas the transition probabilities
for physical states are exponentially suppressed by the global decay. We also
present a brief review on the situation at the so-called exceptional point,
where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.
