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Black Hole Complementarity and ER/EPR

Ning Bao, Grant N. Remmen

TL;DR

This work argues that wormholes must be entangled regardless of asymptotic boundary conditions and that, under black hole complementarity, traversable wormholes function as entanglement-assisted quantum channels requiring preexisting entanglement between stretched horizons. By combining traversable-wormhole protocols with quantum-channel formalism, it shows that such entanglement cannot be generated by the traversal itself and must exist as an initial condition for two-sided wormholes in the same exterior spacetime. This establishes the forward direction of theER/EPR correspondence in broad settings beyond AdS/CFT, linking horizon entanglement to information-theoretic channels. The results illuminate the entanglement structure implied by quantum gravity at horizons and constrain which entanglement patterns can correspond to semiclassical wormholes.

Abstract

We demonstrate that wormholes must be entangled regardless of asymptotic boundary conditions. Assuming black hole complementarity, we argue that traversable wormholes instantiate entanglement-assisted quantum channels and that this entanglement must be present between the stretched horizons as an initial condition prior to traversability. This result demonstrates the forward direction of the ER/EPR conjectures.

Black Hole Complementarity and ER/EPR

TL;DR

This work argues that wormholes must be entangled regardless of asymptotic boundary conditions and that, under black hole complementarity, traversable wormholes function as entanglement-assisted quantum channels requiring preexisting entanglement between stretched horizons. By combining traversable-wormhole protocols with quantum-channel formalism, it shows that such entanglement cannot be generated by the traversal itself and must exist as an initial condition for two-sided wormholes in the same exterior spacetime. This establishes the forward direction of theER/EPR correspondence in broad settings beyond AdS/CFT, linking horizon entanglement to information-theoretic channels. The results illuminate the entanglement structure implied by quantum gravity at horizons and constrain which entanglement patterns can correspond to semiclassical wormholes.

Abstract

We demonstrate that wormholes must be entangled regardless of asymptotic boundary conditions. Assuming black hole complementarity, we argue that traversable wormholes instantiate entanglement-assisted quantum channels and that this entanglement must be present between the stretched horizons as an initial condition prior to traversability. This result demonstrates the forward direction of the ER/EPR conjectures.

Paper Structure

This paper contains 7 sections, 9 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Wormholes and Black Hole Complementarity
  3. Review of Traversable Wormholes
  4. Review of Black Hole Complementarity
  5. Complementarity Implies Entangled Wormholes
  6. Entangled Horizons as an Initial Condition
  7. Discussion

Figures (1)

  • Figure 1: Penrose diagram for the wormhole quantum channel protocol, in a spacetime with arbitrary asymptotics (dashed lines). A NEC-violating shock wave ${\cal S}$ (yellow) drags the left apparent horizon (green) by $\Delta v$. This makes the wormhole traversable by a signal ${\cal T}$ (blue) sent from the right side. In the black hole complementarity picture, this process can be viewed as an entanglement-assisted quantum channel between the left and right stretched horizons ${\cal H}_{L,R}$ (red). In particular, we show that there must exist entanglement between the surfaces $L$ and $R$ (purple) at which ${\cal S}$ and ${\cal T}$ enter their respective stretched horizons; $L$ and $R$ both live in some Cauchy slice $\Sigma$ (gray).