# Pseudo-entropy The pseudo-entropy is a generalisation of entanglement entropy. Instead of the density matrix, one can study a more general quantity called the transition matrix:$\mathcal{T}^{\psi \mid \varphi} \equiv \frac{|\psi\rangle\langle\varphi|}{\langle\varphi |\psi\rangle},$which reduces to the density matrix when $\psi$ and $\varphi$ are the same. The definition of the pseudo-entropy is then similar to that of the entanglement entropy or Renyi entropy:$S^{(n)}\left(\mathcal{T}_A^{\psi \mid \varphi}\right) \equiv \frac{1}{1-n} \log \operatorname{Tr}\left[\left(\mathcal{T}_A^{\psi \mid \varphi}\right)^n\right],$where the subscript $A$ denotes tracing over the complement $A$, which is the region of interest. ## Refs - original - [[2020#Nakata, Takayanagi, Taki, Tamaoka, Wei]] ## Applications - [[2021#Goto, Nozaki, Tamaoka]]: subregion [[0062 Spectral form factor]] from pseudo entropy