[Paper Review] Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes

Adam R. Brown, Hrant Gharibyan+7 more|arXiv (Cornell University)|Nov 14, 2019

Noncommutative and Quantum Gravity TheoriesPhysics and Astronomy32 references56 citations

TL;DR

This paper proposes table-top holographic teleportation protocols inspired by traversable wormholes, introducing teleportation by size and analyzing size winding as a diagnostic for Information transfer in chaotic quantum systems and SYK-like models. It outlines experimental realizations in Rydberg atom arrays and trapped ions.

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.

Motivation & Objective

• Motivate studying quantum gravity phenomena in lab-accessible quantum systems through holographic teleportation concepts.
• Introduce teleportation by size as a mechanism for information transfer in chaotic many-body systems.
• Differentiate high-temperature, low-capacity teleportation from low-temperature, high-capacity, wormhole-like teleportation.
• Define and explore size winding as a boundary-operator diagnostic of traversable-wormhole physics.
• Propose concrete experimental platforms and protocols to realize these phenomena.

Proposed method

• Model a two-sided system in a thermofield double state with left and right scrambling Hamiltonians.
• Use backward and forward time evolution on the left, a left-right coupling e^{igV}, and forward evolution on the right to realize teleportation circuits.
• Introduce and analyze two mechanisms: state transfer by size-dependent phase and size winding.
• Define the winding size distribution q(l) and its Fourier transform g to bound teleportation fidelity F.
• Derive general fidelity bounds for entanglement fidelity in terms of the size distribution Fourier transform tilde{q}_l(g).
• Relate to holographic pictures via size, momentum, and emergent geometry concepts.

Experimental results

Research questions

• RQ1 Can chaotic quantum systems transmit information via holographic-like teleportation without a geometric wormhole?
• RQ2 How does operator growth (size distribution) facilitate information transfer in left-right coupled systems?
• RQ3 What is size winding and how does it signal traversable-wormhole-like behavior in boundary theories?
• RQ4 Under what conditions (temperature, scrambling, system size) can high-fidelity teleportation occur?
• RQ5 How can these protocols be realized experimentally in Rydberg atom arrays and trapped-ion platforms?

Key findings

• Teleportation by size identifies two distinct mechanisms: high-temperature, low-capacity state transfer that does not require a geometric wormhole, and low-temperature, high-capacity teleportation that corresponds to wormhole-like transmission.
• Size winding provides a boundary-theory diagnostic linking operator growth to momentum-like behavior and potential traversability in holographic models.
• For Haar-random or generic scrambling dynamics, the sandwiched coupling e^{igV} can approximate the desired transfer unitary in certain regimes, enabling high-fidelity transfer under appropriate g.
• In the infinite-temperature case, a single-qubit transfer can be achieved with perfect fidelity at g =  (pi) in idealized models; more generally, fidelity is bounded and analyzed via the Fourier transform of the size distribution.
• The paper provides explicit formulas and bounds (e.g., Eq. 3, Eq. 11, Eq. 12, Eq. 14, Eq. 15) for the state/output fidelity in terms of the size distribution and its Fourier transform.
• Experimental proposals are outlined for Rydberg atom arrays and trapped ions to realize the proposed teleportation circuits.