Diagnosing collisions in the interior of a wormhole

TL;DR

This work casts the interior meeting of signals in an ER=EPR wormhole as the overlap of growing perturbations in a quantum circuit that prepares the entangled TFD state. It introduces a renormalized operator size, computable as a six-point correlator, to diagnose collisions from outside observers. Using a Schwarzian/Schwarzian-like gravity framework, the authors derive an explicit F6 form that grows exponentially with negative circuit time and saturates at scrambling time, aligning with a bulk JT gravity calculation. The results provide a concrete, dynamical diagnostic of interior events without entering the wormhole and emphasize the singularity's role in constraining late-time collisions, while outlining open questions for geometries without singularities.

Abstract

Two distant black holes can be connected in the interior through a wormhole. Such a wormhole has been interpreted as an entangled state shared between two exterior regions. If Alice and Bob send signals into each of the black holes, they can meet in the interior. In this letter, we interpret this meeting in terms of the quantum circuit that prepares the entangled state: Alice and Bob sending signals creates growing perturbations in the circuit, whose overlap represents their meeting inside the wormhole. We argue that such overlap in the circuit is quantified by a particular six-point correlation function. Therefore, exterior observers in possession of the entangled qubits can use this correlation function to diagnose the collision in the interior without having to jump in themselves.

Figures (5)

• Figure 1: We model the dynamical evolution of the entangled thermofield double state by a simple quantum circuit: at each time step the shared qubits (black lines) are randomly grouped into $\frac{S}{2}$ pairs, and on each pair a randomly chosen 2-qubit gate (orange dots) is applied.
• Figure 2: Left: The red (pink) arrow represents the extra qubit due to Alice's (Bob's) perturbation. Any qubits that interact directly or indirectly with these perturbations, get perturbed relative to the original circuit describing the thermofield double state. When $t_{wL}+t_{wR}>0$, the two perturbations do not have overlap in the quantum circuit. Right: Correspondingly, the signals sent into the bulk hit the singularity before they have a chance to meet inside the wormhole.
• Figure 3: Left: When $t_{wL}+t_{wR}<0$, the two perturbations have overlap in the quantum circuit. Right: In the bulk geometry this corresponds to a collision inside the wormhole.
• Figure 4: We consider the perturbed state at left and right times $a$ and $b$. The correlator \ref{['correlator']} can be approximated by the bulk geodesic distance between these anchor points.
• Figure 5: The complex time contour representing the correlator \ref{['correlator']}. Real time goes towards the right.