On the Page curve under final state projection

TL;DR

This paper investigates how final state projection in two-dimensional conformal field theories influences the entanglement entropy evolution, revealing a Page curve-like behavior that may shed light on black hole information paradox resolution.

Contribution

It introduces a novel analysis of the Page curve in the context of final state projection within 2D CFTs, connecting quantum entanglement dynamics to black hole information issues.

Findings

Pseudo-entropy exhibits a Page curve-like behavior.

Final state projection affects entanglement evolution.

Results suggest a potential resolution to the information paradox.

Abstract

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