Page curve under final state projection

The black hole singularity plays a crucial role in formulating Hawking's information paradox. global spacetime analysis may be reconciled with unitarity by imposing final state boundary condition on the spacelike singularity. Motivated proposal, we explore effect of projection two dimensional conformal field theories. We calculate time evolution under postselection employing real part pseudoentropy to estimate amount quantum entanglement averaged over histories between initial and states. find that this quantity possesses Page-curve-like behavior.