⚛️ high-energy theory

Holographic Entanglement Propagation Through Wormholes

This paper demonstrates that inserting a local operator into one of two entangled CFTs enables energy and entanglement transfer through a holographic wormhole via a non-unitary, measurement-like process akin to quantum teleportation, which uniquely enhances mutual information rather than suppressing it through scrambling.

Original authors: Kazuki Doi, Liang Li, Ung Nguyen, Tadashi Takayanagi

Published 2026-01-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kazuki Doi, Liang Li, Ung Nguyen, Tadashi Takayanagi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Two Rooms and a Secret Tunnel

Imagine you have two identical, separate rooms (let's call them Room 1 and Room 2). In the world of physics described in this paper, these rooms represent two separate universes or "fields" of energy.

Usually, if you do something in Room 1, it stays in Room 1. You can't shout across to Room 2, and you can't throw a ball there. They are causally separated.

However, this paper explores a special setup where these two rooms are secretly connected by a tiny, temporary tunnel (a "wormhole"). This tunnel isn't a permanent highway; it's more like a small, localized bridge that appears at a specific spot and time.

The Experiment: A Localized "Handshake"

The researchers set up a scenario where they "handshake" these two rooms at a specific point in time and space.

The Setup: They create a state where the two rooms are deeply entangled (connected) only at a tiny spot, like gluing two pieces of paper together at a single dot.
The Action: In Room 1, they drop a "pebble" (a local energy excitation). In normal physics, this pebble would just ripple out in Room 1.
The Surprise: Because of the secret tunnel (the wormhole), a tiny bit of that pebble's energy and information actually makes it through the tunnel and appears in Room 2.

The Magic Trick: Quantum Teleportation

The paper argues that this isn't just energy leaking; it's actually a form of Quantum Teleportation.

Think of it like this:

Usually, to move a secret message from Room 1 to Room 2, you need a physical carrier (like a runner).
In this experiment, the "runner" doesn't exist. Instead, the researchers perform a special measurement (a "projection") on the system.
Because of the way the two rooms are glued together, this measurement acts like a magic trick. It effectively "teleports" the state of the pebble from Room 1 to Room 2.
The paper notes that this works best when the "pebble" is slightly fuzzy (regulated) rather than a sharp, infinite point. The fuzzier the pebble (within limits), the more successful the teleportation.

The "Anti-Scrambling" Effect

In the world of quantum physics, there is a famous concept called Scrambling. Imagine dropping a drop of red ink into a glass of water. The ink spreads out, mixes, and becomes impossible to separate. This is what usually happens when you disturb an entangled system: the connection gets messy and the information gets lost in the noise.

This paper found something strange and opposite: Descrambling.

The Scenario: They dropped their "pebble" into the system.
The Result: Instead of the connection between the rooms getting messier, the connection actually got stronger for a while. The mutual information (how much the rooms know about each other) increased.
The Analogy: Imagine you have two people whispering secrets to each other. Usually, if you shout at one of them, they stop listening to each other. But in this specific setup, shouting at one person actually made them whisper louder and clearer to the other person for a brief moment. The "tunnel" allowed the information to flow so efficiently that it boosted their connection rather than breaking it.

Why Does This Happen?

The paper explains that this is possible because the process of dropping the "pebble" (the local operator) is not a standard, reversible game.

In standard physics, everything is "unitary," meaning you can always rewind the movie to see exactly how things happened.
Here, the process is like a measurement. It's like taking a photo. Once you take the photo, you can't "un-take" it. This irreversible act allows the signal to bypass the usual rules (like the event horizon of a black hole) and travel through the wormhole.

Summary of Findings

Energy Transfer: Energy can travel from one universe to another through a localized wormhole, but only if the "tunnel" and the "pebble" are sized correctly.
Teleportation: This transfer is mathematically identical to quantum teleportation, where a state is moved without a physical carrier.
Boosted Connection: Contrary to the usual rule that disturbances destroy connections, this specific setup can temporarily enhance the connection between the two universes.
The Limit: This effect is delicate. If the "pebble" is too sharp or the "tunnel" is too small, the effect fades, and the system returns to normal behavior (or the connection gets scrambled).

In short, the paper demonstrates that by carefully gluing two universes together at a single point and performing a specific type of measurement, you can create a temporary bridge that allows information to teleport across, effectively turning a "scrambling" event into a "boosting" event.

Technical Summary: Holographic Entanglement Propagation Through Wormholes

Problem Statement
The paper addresses the mechanism of energy and quantum entanglement transfer between two identical, locally entangled Conformal Field Theories (CFTs). While the AdS/CFT correspondence provides a geometric interpretation of entanglement via wormholes (specifically the eternal AdS black hole), standard setups often treat the two CFTs as causally separated, preventing signal propagation across the horizon. The authors investigate whether a local operator insertion in one CFT can induce a transfer of energy and information to the other CFT through a "localized" wormhole, and how this process relates to quantum teleportation and the scrambling of information.

Methodology
The authors construct a model involving two 2D CFTs (CFT $_1$ and CFT $_2$ ) coupled via a "localized thermofield double (TFD) state." This state is prepared at time $t=t_M$ and location $x=0$ by gluing two small holes in the Euclidean path integral of the two CFTs. The size of the entanglement region is regulated by a parameter $s$ , and the effective temperature is controlled by $\beta$ .

Setup: A local operator excitation $O$ is inserted into CFT $_1$ at $t=0, x=x_P$ . This excitation is regularized by a damping factor $e^{-\delta H}$ , where $\delta$ represents the spatial size of the excitation. The condition $0 < \delta < s$ is assumed for computational tractability.
Holographic Dual: In the gravity dual (AdS $_3$ /CFT $_2$ ), the localized TFD state corresponds to a localized wormhole (or a falling black hole) propagating at the speed of light. The operator insertion is treated as a non-unitary operation, interpreted as a regularized projection measurement.
Calculations:
- Energy Transmission: The authors compute the energy density stress tensor in both CFTs using holographic CFT techniques (mapping the torus geometry to a cylinder/annulus) and free scalar CFT calculations (using Ward identities on the torus).
- Entanglement Entropy: They calculate the time evolution of entanglement entropy ( $S_A, S_B$ ) and mutual information ( $I_{AB}$ ) for single and double-interval subsystems. This involves evaluating four-point functions of twist operators in the cyclic orbifold theory $CFT_n/Z_n$ using the heavy-heavy-light-light (HHLL) approximation and saddle-point methods.
- Regimes: The analysis considers both the "disconnected" and "connected" phases of the entanglement entropy, corresponding to different geodesic configurations in the bulk.

Key Contributions and Results

Signal Propagation via Wormhole: The paper demonstrates that for non-zero $\delta$ , signals (energy and entanglement) can propagate from CFT $_1$ to CFT $_2$ . This occurs because the Euclidean path integral description of the local operator insertion is not a unitary evolution, effectively allowing the signal to penetrate the black hole horizon.
Connection to Quantum Teleportation: The authors argue that the transmission mechanism is a form of quantum teleportation. When the ratio $\delta/s$ is large (specifically $\delta \simeq s$ ), the operation acts as a projection onto the ground state, successfully teleporting the state $O|0\rangle$ from CFT $_1$ to CFT $_2$ . The efficiency of this transmission increases as $\delta/s$ increases.
Energy Transmission: Numerical evaluations show that energy is transmitted to the second CFT, though the amplitude is significantly smaller than the energy remaining in the first CFT. The transmission rate is controlled by the ratio $\delta/s$ and the size of the wormhole $s$ .
Descrambling vs. Scrambling: A central finding is the observation of a phenomenon opposite to scrambling.
- Scrambling: In many configurations, the mutual information between subsystems decreases, consistent with standard chaotic behavior.
- Descrambling: Under specific geometric conditions (where the local operator's right-moving mode spreads to the second CFT while the left-moving mode remains in the first), the mutual information is enhanced ( $\Delta I_{AB} > 0$ ). This "descrambling" effect occurs because the local operator excitation creates new correlations that are transmitted through the wormhole, temporarily increasing the mutual information beyond the background TFD value.
Free vs. Holographic CFTs: The results for free bosonic CFTs qualitatively match those of holographic CFTs, validating the saddle-point approximation used for the holographic calculations on the torus.

Significance and Claims
The paper claims to provide the first explicit, analytically tractable model demonstrating that local operator insertions in a holographic setup can facilitate signal propagation across an AdS wormhole, a process interpreted as quantum teleportation.

The authors emphasize that this transmission is possible because the insertion of a local operator is a non-unitary process (a regularized projection measurement), distinguishing it from standard unitary time evolution where such horizon-crossing signals are forbidden in eternal black hole geometries. Furthermore, the paper highlights the counter-intuitive result that local excitations can enhance, rather than suppress, mutual information in specific regimes, offering a new perspective on the interplay between quantum operations, entanglement, and holographic geometry. The work suggests that the ability of the localized TFD state to transmit information is directly tied to these non-unitary operational aspects of quantum entanglement.