Holographic Entanglement Propagation Through Wormholes

TL;DR

This work addresses how two identical CFTs, locally entangled, exchange energy and quantum information when a local operator is inserted. It develops a concrete holographic model with a localized thermofield double state, interpreting the Euclidean preparation as a non-unitary teleportation-like operation that transmits excitations via an AdS wormhole. Energy density and entanglement entropy calculations, in both holographic and free CFTs, show signal propagation through the wormhole and a bipartite entanglement pattern evolving across time, with mutual information sometimes enhanced (descrambling) rather than suppressed. The results illuminate how non-unitary local operations can mediate traversable-like information transfer in holographic settings and have implications for understanding entanglement structure across wormholes and quantum teleportation in CFTs.

Abstract

We study how energy and quantum entanglement are transferred when two identical CFTs are entangled locally. This is probed by considering a local operator insertion in one of the CFTs. When the CFTs have holographic duals via the AdS/CFT correspondence, the transfer happens through an AdS wormhole that allows signal propagation even beyond the horizon from one AdS boundary to the other; we demonstrate this in explicit CFT calculations. We argue that this transmission is possible because the insertion of a local operator is not a unitary process but a regularized version of projection measurement, and that this is interpreted as quantum teleportation. We also find that this leads to a phenomenon opposite to scrambling, where mutual information, instead of being suppressed, gets enhanced by the insertion of a local operator excitation.

Figures (34)

• Figure 1: A sketch of the Euclidean path integral description of density matrix $\rho_2$ in CFT$_2$ (left) and a quantum circuit description of $\rho_2$ (right). If $\delta$ is large, the operation surrounded by the dashed rectangle acts like a projection to the ground state and thus this becomes quantum teleportation of the state ${\cal O}|0\rangle$ in CFT$_1$ to that in CFT$_2$.
• Figure 2: Euclidean path integral over a plane with two holes inserted. We prepare two copies of the same sheet and identify the circles.
• Figure 3: The $(w,\bar{w})$ strip. The left and right edges of this strip correspond to the circles in the original $(X,\bar{X})$ geometry. The wormhole, i.e. the torus, is obtained by taking two copies of the strip and identifying the left and right edges of one of the copies to the corresponding edges of the other.
• Figure 4: Annulus formed by decompactifying the torus. CFT1 is mapped to the right half and CFT2 is mapped to the left half.
• Figure 5: The Lorentzian setup of the local operator quench, represented by the operator insertion $\mathcal{O}$ at $(t,x)=(0,x_P)$. The background is defined by the localized TFD state inserted at $(t,x)=(t_M,0)$.