  In this paper, we explore the concept of pseudo R\'enyi entropy within the
context of quantum field theories (QFTs). The transition matrix is constructed
by applying operators situated in different regions to the vacuum state.
Specifically, when the operators are positioned in the left and right Rindler
wedges respectively, we discover that the logarithmic term of the pseudo
R\'enyi entropy is necessarily real. In other cases, the result might be
complex. We provide direct evaluations of specific examples within
2-dimensional conformal field theories (CFTs). Furthermore, we establish a
connection between these findings and the pseudo-Hermitian condition. Our
analysis reveals that the reality or complexity of the logarithmic term of
pseudo R\'enyi entropy can be explained through this pseudo-Hermitian
framework.
  Additionally, we investigate the divergent term of the pseudo R\'enyi
entropy. Interestingly, we observe a universal divergent term in the second
pseudo R\'enyi entropy within 2-dimensional CFTs. This universal term is solely
dependent on the conformal dimension of the operator under consideration. For
$n$-th pseudo R\'enyi entropy ($n\ge 3$), the divergent term is intricately
related to the specific details of the underlying theory.
