ER = EPR revisited: On the Entropy of an Einstein-Rosen Bridge

TL;DR

This paper revisits the entropy-area relationship for Einstein-Rosen bridges, proposing a new bound on quantum information in black holes and analyzing the nature of their mixed states using advanced gravity techniques.

Contribution

It introduces a new entropy bound for ER bridges and demonstrates that black hole quantum information is topologically protected, supported by calculations in AdS3 and JT gravity.

Findings

Entropy of an ER bridge is bounded by A/4G_N.

Typical black hole states are entangled 'thermo-mixed double' states.

Black hole quantum information exhibits topological protection.

Abstract

We propose a new link between entropy and area: an eternal black hole with an ER bridge with cross-section $A$ can carry a macroscopic amount of quantum information, or be in a mixed state, with entropy bounded by $S \leq A/4G_N$. We substantiate our proposal in the context of AdS3 and JT gravity, by using the Island prescription and replica wormhole method for computing the black hole entropy. We argue that the typical mixed state of a two sided black hole takes the form of an entangled `thermo-mixed double' state with only classical correlations between the two sides. Our result for the von Neumann entropy of a post-Page time two-sided black hole is smaller by a factor of two from previous answers. Our reasoning implies that black hole quantum information is topologically protected, similar to the information stored inside a topological quantum memory.