Does Considering Quantum Correlations Resolve the Information Paradox?

TL;DR

This paper investigates whether quantum correlations during black hole evaporation can resolve the information paradox, concluding that such corrections are insufficient to restore unitarity and align with existing literature.

Contribution

It generalizes the correction bounds to Hawking states, providing a quantitative measure of entanglement entropy change and confirming the limitations of quantum correlations in resolving the paradox.

Findings

Small quantum correlations do not restore unitarity.

Generalized bounds on entanglement entropy show significant deviation from Page curve.

Corrections in the form of Bell pairs are insufficient for resolution.

Abstract

In this paper, we analyze whether quantum correlations between successive steps of evaporation can open any way to resolve the black hole information paradox. Recently a celebrated result in literature shows that `small' correction to leading order Hawking analysis fails to restore unitarity in black hole evaporation. We study a toy qubit model of evaporation allowing small quantum correlations between successive steps and verify the previous result. Then we generalize the concept of correction to Hawking state by relaxing the `smallness' condition. Our result generates a nontrivial upper and lower bound on change in entanglement entropy in the evaporation process. This gives us a quantitative measure of correction that would mathematically facilitate restoration of unitarity in black hole evaporation. We then investigate whether this result is compatible to the established physical constraints of unitary evolution of a state in a subsystem. We find that the generalized bound on entanglement entropy leads to significant deviation from Page curve. This leads us to agree with the recent claim in literature that no amount of correction in the form of Bell pair states would lead to any resolution to the information paradox.