  As a generalization of entanglement entropy, pseudo entropy is not always
real. The real-valued pseudo entropy has promising applications in holography
and quantum phase transition. We apply the notion of pseudo-Hermticity to
formulate the reality condition of pseudo entropy. We find the general form of
the transition matrix for which the eigenvalues of the reduced transition
matrix possess real or complex pairs of eigenvalues. Further, we construct a
class of transition matrices for which the pseudo (R\'enyi) entropies are
non-negative. Some known examples which give real pseudo entropy in quantum
field theories can be explained in our framework. Our results offer a novel
method to generate the transition matrix with real pseudo entropy. Finally, we
show the reality condition for pseudo entropy is related to the Tomita-Takesaki
modular theory for quantum field theory.
