ER=EPR, GHZ, and the Consistency of Quantum Measurements

TL;DR

ER=EPR investigates whether entanglement between black holes implies Einstein-Rosen bridges and how this picture aligns with standard quantum mechanics. The paper argues heuristically that ER=EPR is compatible with RT and uses GHZ entanglement to resolve potential observer inconsistencies, introducing the GHZ-core as a necessary non-classical feature. It then recasts entanglement as a resource, showing how teleportation can be visualized as ERB-based transfer of quantum information, with classical communication completing the protocol. The work highlights that geometry and quantum information are deeply intertwined and that multipartite entanglement shapes the structure of wormholes.

Abstract

This paper illustrates various aspects of the ER=EPR conjecture.It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges. The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern. The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.

Figures (8)

• Figure 1: A special slice of ADS with two objects. The blue line represents the RT surface for calculating entanglement entropy between the left and right semicircles. The construction fails to account for possible entanglement between the objects.
• Figure 2: The RT surface for two black holes contained in ADS. If the black holes are not entangled then the topology is trivial as in the left panel. If they are entangled the validity of the RT prescription requires a wormhole between them.This is shown in the middle and right panels.
• Figure 3: The entangled systems are clouds gas composed of small black holes.
• Figure 4: On the left side the signals originate at the boundary at $t=0.$ They barely meet before they reach the singularity. In the right figure Charlie creates a signal by acting with a precursor which effectively introduces the signal at point $a.$ No interaction between Charlie's side and Bob's side is necessary in order for their signals to meet and interact in the ERB.
• Figure 5: Tensor network representation of $GHZ$-entangled black holes. The upper figure shows the tensor $T_{ijk}$ representing the basic $ghz$-triplet. The lower left shows tensor network for a product of $ghz$-triplets. The lower right illustrates the evolution of the tensor network with time. The growth of the tensor network represents the growth of complexity.