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

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.