SYK model based $β$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation

TL;DR

The paper demonstrates a SYK-based implementation of the Wormhole-Inspired Teleportation Protocol (WITP) in a two-sided thermofield-double system, quantifying information transfer through a traversable wormhole analogy. By contrasting SYK dynamics with a TFIM benchmark, it shows that chaotic many-body dynamics yield higher teleportation fidelity, especially for single-qubit basis states, and introduces a Pauli-stabilizer fidelity framework for two-qubit Bell-state teleportation. Fidelity is shown to depend sensitively on temperature $eta$, coupling $g$, traversal time $t$, and the Majorana operator distance, with a clear coherence scale $eta_c$ governing decoherence, and a Bell-state fidelity peak at infinite temperature around $eta=0$ (e.g., $ ext{F}_{ ext{Bell}} o 0.83$). Collectively, this work provides a finite-$N$ numerical testbed connecting quantum chaos, holographic duality, and ER=EPR phenomenology in a concrete many-body quantum simulator setting.

Abstract

We implement the Wormhole-Inspired Teleportation Protocol (WITP) in a pair of coupled Sachdev-Ye-Kitaev (SYK) models prepared in a thermofield-double state, forming a quantum analog of a traversable wormhole. By varying parameters (temperature, coupling strength, insertion site, and traversal time), we compare the teleportation fidelity against an analogous protocol using a transverse-field Ising model. We find that the chaotic SYK system consistently yields higher teleportation fidelity than the TFIM model, reflecting the SYK Hamiltonian's pronounced many-body chaos. These enhanced fidelities arise from the SYK's effectively random-matrix dynamics, which improve coherent information transfer through the wormhole channel. Unlike prior single-qubit benchmarks based on basis state inputs, the present work defines and evaluates a genuinely quantum-state fidelity for a maximally entangled two-qubit Bell input, using a Pauli-stabilizer formalism that captures entanglement-phase coherence. Our central result is achieved by teleporting a maximally entangled two-qubit Bell state through the wormhole. We introduce a Pauli-stabilizer fidelity measure for the two-qubit message and demonstrate that the Bell-state protocol produces a substantial fidelity boost compared to single-qubit teleportation. Furthermore, we examine the time-resolved fidelity for both single-qubit and two-qubit messages, revealing distinct fluctuation patterns that deepen the understanding of dynamical many-body teleportation processes. Finally, we present an argument that our Bell-state WITP simulations provide a concrete numerical testbed for aspects of the ER=EPR conjecture, by mapping entanglement structure and thermal/coupling dependence to traversability diagnostics in an emergent wormhole geometry.

Figures (15)

• Figure 1: Quantum circuit representation of Wormhole-Inspired teleportation protocol. L and R are the two throats of a geometric wormhole initialized in the TFD state. On the left side, we have negative time evolution followed by the swapping in of the message qubit. Subsequently, there is time evolution through the L side first and coupling with the R side, followed by its traversal throughout the system, only to be traced out from the R throat.
• Figure 2: Wormhole-inspired teleportation protocol in AdS/CFT Geometry picture. In order to avoid the transmission of our message straight into the singularity, from L throat, we start with a negative time evolution, followed by the swapping in of the message and positive time evolution. The coupling introduces a "shockwave" which propels the message out through the R throat of the wormhole.
• Figure 3: Teleportation fidelity for N=6 SYK Hamiltonian with $\Delta^{(0,1)}$ operator for a range of $\beta$ values. Fidelity is maximum for $\beta=0$ and reduces considerably for increasing values of $\beta$.
• Figure 4: Teleportation fidelity for N=6 SYK Hamitonian with $\Delta^{(0,2)}$ operator for a range of $\beta$ values. Here, fidelity is minimum for $\beta=0$ and peaks at $\beta=20$, decreasing thereafter.
• Figure 5: Comparison of teleportation fidelity for N=6 SYK Hamiltonian based Model and N=6 TFIM Hamiltonian Based model sweeping over values of $g$ at $\beta = 0$.