Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes

TL;DR

The paper proposes tabletop experiments to probe quantum gravity-inspired phenomena by implementing holographic teleportation between entangled many-body systems. It introduces teleportation by size, with two mechanisms: a high-temperature, non-geometric regime and a low-temperature, geometry-linked regime characterized by size winding, along with fidelity bounds framed by the size distribution Fourier transform. The authors connect boundary-size dynamics to bulk momentum and discuss regimes where semiclassical geometry emerges or fails, including the possibility of wormhole tomography. Practical realizations are outlined for Rydberg atom arrays and trapped ions, with considerations of state preparation, time reversal, and weak left-right coupling. This work aims to bridge quantum information, chaos, and gravity, offering experimentally accessible probes of holographic duality and emergent spacetime.

Abstract

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable wormhole constructions of [1,2]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. In addition, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions.

Figures (5)

• Figure 1: The circuits considered in this paper, with $H_L = H_R^T$. Downward arrows indicate acting with the inverse of the time-evolution operator. In both protocols, the goal is to transmit information from the left to the right. The (a) state transfer protocol calls for us to discard the left message qubits ($A_L$) and replace them with our message $\Psi_{\mathrm{in}}$. The output state on the right then defines a channel applied to the input state. The (b) operator transfer protocol calls for the operator $O$ to be applied to $A_L$. Based on the choice of operator, the output state on the right is modified, similar to a perturbation-response experiment.
• Figure 2: Penrose diagram of wormholes. Left: Without the coupling, a message or particle inserted at early times on the left passes through the left horizon, and hits the singularity (the top line of the diagram). Right: In the presence of the left-right coupling, the message hits the negative energy shockwave (the thick blue line) created by the coupling. The effect of the collision is to rescue the message from behind the right horizon.
• Figure 3: (a): Infinite-temperature holographic teleportation circuit, with $U=e^{-iHt}$. (b): An equivalent circuit to (a) after circuit manipulations. (c): Result of replacing the trace by projecting the carrier qubits onto $\ket {\phi^+}$. When the teleportation has high fidelity, this projection has a negligible effect on the final state. For many systems of interest, the operator $\tilde{S}$ enclosed in the dashed rectangle approximately implements the unitary defined in \ref{['eq:hol_tel_def_cond']} for some appropriate $g'$.
• Figure 4: A short summary of teleportation by size, discussing different systems, different patterns of operator growth, and consequence of each growth pattern for signal transmission. Blue: Initial operator-size distribution. Red: Winding size distribution of the time-evolved operator.
• Figure 5: Expectation value of $Z_{1R}$ after injection of $Z_{1L}=1$ state on the left system. Black dots are direct numerical simulation of the protocol in the quantum kicked Ising model with $n=7$ spins on the left and right and with $J=b=\pi/4$ and $h_i$ drawn from a box distribution of width $.5$. Left: Signal at fixed large time as a function of $g$. The black circles are the exact numerical simulation. The red curve is the theory prediction in Eq. \ref{['eq:zavg_infT']}. Right: Signal at fixed $g$ as a function of time step. The black circles are the exact numerical simulation. The red curve is a crude approximation where we assume Eq. \ref{['eq:zavg_infT']} holds at all times with the effective system size replaced as $n \rightarrow \min(t+1,n)$.

Theorems & Definitions (4)

• Lemma 1
• proof
• Lemma 2
• proof