Holographic Entanglement Propagation through Wormholes Demonstrates Signal Transfer Beyond Boundaries

Researchers are investigating how entanglement propagates between two quantum systems connected by a theoretical wormhole, offering new insights into the fundamental nature of spacetime and quantum gravity. Kazuki Doi, Liang Li, and Ung Nguyen, from the Center for Gravitational Physics and Quantum Information at Kyoto University, alongside Tadashi Takayanagi from the Inamori Research Institute for Science, demonstrate this propagation using calculations based on the AdS/CFT correspondence, revealing that information can travel through these wormholes even beyond conventional boundaries. Their work suggests that local operator insertions act not as unitary processes, but as a form of quantum teleportation, and surprisingly exhibit behaviour contrary to quantum scrambling by actually enhancing mutual information between the systems. This finding could fundamentally alter our understanding of information transfer and entanglement in strongly coupled quantum systems and potentially shed light on the elusive connection between gravity and quantum mechanics.

Wormhole-mediated quantum teleportation between CFTs is a fascinating

This unconventional approach facilitates the transmission, effectively acting as a form of quantum teleportation between the two systems. The study establishes a model involving two-dimensional CFTs entangled locally, achieved by ‘gluing’ small holes in the CFTs within a Euclidean path integral description. This localized entanglement is parameterized by a UV regulator, s, and an effective inverse temperature, β, controlling the conformal dimensions of participating local operators. When a local excitation, denoted by operator O, is introduced into one CFT, the team observed its transmission to the other under time evolution, meticulously computing the energy density and entanglement entropy to track the process.

This enhancement is directly linked to the propagation of Quantum entanglement and provides a novel perspective on how information can be transferred in these systems. Furthermore, the work opens avenues for understanding quantum operations beyond local operations and classical communications (LOCC), traditionally central to quantum information theory. By connecting holographic entanglement entropy with operational aspects of quantum entanglement, the study provides a new framework for analyzing quantum field theories and quantum gravity. This breakthrough differs from previous traversable wormhole models relying on double trace deformations or Janus deformations, offering a unique mechanism for signal transmission. Future research will focus on exploring the implications of these findings for understanding the fundamental relationship between entanglement, gravity, and quantum information.

Entanglement and Signal Transfer via AdS Wormholes

This localized entanglement was realised via gluing two small holes in the CFTs, with the spatial size regulated by a parameter ‘s’ and the effective inverse temperature controlled by ‘β’. The team analytically calculated the contribution to entanglement entropy and mutual information from both the localised time-dependent fidelity (TFD) state and the local operator quench. This work pioneered a method for modelling quantum entanglement and energy transmission between CFTs as a class of quantum operations. The team employed Euclidean path integral descriptions to represent density matrices, and a quantum circuit approach to visualise the process. The study demonstrated that for non-vanishing δ, the operation resembles quantum teleportation from CFT1 to CFT2, with transmission success increasing as δ grows. This approach enables the observation of signal propagation between causally separated CFTs, a feature absent in eternal AdS black hole models.

Wormhole Teleportation Enhances Mutual Information between distant quantum

Data shows that this leads to a counterintuitive phenomenon, enhancing mutual information via the local operator excitation, rather than suppressing it as expected in scrambling scenarios. The research team focused on the torus partition function, identifying a phase transition at β = π, corresponding to the Hawking-Page transition in its gravitational dual. By selecting a specific phase, the torus was approximated as an infinite cylinder through decompactification of either the temporal or spatial direction. The study concentrated on the high temperature phase, β < π, decompactifying the spatial direction using the conformal map ζ = e^(πiβw), resulting in an annulus.

Correlation functions, calculable on the resulting Euclidean plane, were then conformally transformed back to the original (X, X)-coordinates in both CFTs. Measurements confirm that on the time slice connecting the CFTs, their spatial orientations are opposite. To understand quantum entanglement within the localized TFD state, scientists analysed the entanglement between four points at time t: P1, Q1 in CFT1 and Q2, P2 in CFT2. The team measured that the localized TFD state generates bipartite quantum entanglement for these point pairs. The normalization was chosen such that ⟨Ψquench(t)|Ψquench(t)⟩12 = 1.

The team found that the reduced density matrix in CFT2 is given by ρ2 = N^2·Tr1{e−δH(1)O(xP, −t)eδH(1)|Ψ(t −tM)⟩12⟨Ψ(t −tM)|12eδH(1)O†(xP, −t)e−δH(1)}. However, when δ ≃ s and |xP + tM| ≪ δ, the channels Oj × O† and O × Oi dominate, localizing the summations over i and j when Oi = Oj = O. Consequently, the density matrix approximates ρ2 ≃ |O⟩⟨O|, demonstrating successful teleportation of the local excitation from CFT1 to CFT2. The team also calculated the energy density distribution in both CFTs, paving the way for further analysis of locally entangled systems with local operator excitations.

Wormhole Teleportation via Local Operator Insertion

Calculations within the CFT framework demonstrate this phenomenon explicitly. The study details the evolution of entanglement entropy and mutual information, considering both single and double-interval subsystems, and provides analytical and numerical evaluations to support these findings. This work establishes a model for transmitting quantum entanglement and energy between two CFTs, offering an analytically tractable system for exploring quantum operations. The significance lies in bridging concepts from quantum information theory, such as LOCC and teleportation, with high-energy physics and holographic duality. Authors acknowledge limitations stemming from the use of parameters like s and δ as UV regulators, which introduce specific scales into the analysis. Future research could explore the robustness of these findings with different regularization schemes or investigate the implications for more complex systems and geometries, potentially furthering our understanding of quantum gravity and information transfer in extreme environments.