Minimal system size for verifiable traversable-wormhole teleportation
In plain words
Two coupled copies of the SYK model can teleport a quantum bit in a way that mirrors a signal crossing a wormhole in a dual gravity theory. A 2022 experiment claimed this with a heavily simplified model, and critics argue that model is too small and too regular to support the claim.
Precise statement
The protocol prepares two SYK systems in a thermofield-double state, inserts a qubit, applies a weak coupling of strength $\mu$, and predicts a teleportation signal peaked near the scrambling time with operator size winding. Jafferis et al. (Nature 2022, doi:10.1038/s41586-022-05424-3) used a learned 7-qubit Hamiltonian; Kobrin, Schuster, Yao (arXiv:2302.07897) argued that it does not thermalize and matches SYK only for the training operators. Determine the minimal N and Hamiltonian class (dense or sparse SYK) for which the signal, its $\mu$ dependence and size winding are distinguishable from generic small or commuting models. Answer: $N_{\mathrm{min}}$ with explicit criteria, and whether present hardware reaches it.
What would settle it
Numerics of the protocol at increasing N locating where gravitational signatures separate from generic ones, followed by an experiment at that N.
Status in the literature
Claimed in 2022 and disputed in a 2023 comment by Kobrin, Schuster and Yao.