Constructible reality condition of pseudo entropy via pseudo-Hermiticity

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