# 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:$\tau \equiv \frac{|\psi\rangle\langle\varphi|}{\langle\varphi |\psi\rangle},$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 [[0293 Renyi entropy|Renyi entropy]]:$S^{(n)}(\tau) \equiv \frac{1}{1-n} \log \operatorname{Tr}\left[\tau_A^n\right],$where the subscript $A$ denotes tracing over the complement of $A$ to get the reduced transition matrix for the subregion of interest $A$. ## Refs - original - [[2020#Nakata, Takayanagi, Taki, Tamaoka, Wei]] ## Applications - [[2021#Goto, Nozaki, Tamaoka]]: subregion [[0062 Spectral form factor|spectral form factor]] from pseudo entropy - [[2026#Kanda, Takayanagi, Wei]]: computing pseudo-entropy using BCFT methods, with results matching those of holographic calculations