No chaos required: traversable wormhole signals survive 98% coupling deletion

Abstract

The traversable wormhole protocol in coupled Sachdev-Ye-Kitaev (SYK) systems produces a transmission signal C(t) widely interpreted as evidence of holographic dynamics. Recent work has questioned this interpretation, showing that similar signals arise in generic thermalizing systems. We address what the signal actually probes by systematically destroying quantum chaos in the SYK model via random coupling deletion, while monitoring the transmission signal across the chaos-to-integrable transition. Using exact diagonalization of the doubled SYK model at N=10 with 50 disorder realizations per sparsity, supplemented by Krylov-subspace extensions to N=20, we find that the ensemble-averaged peak height varies by less than 1.1% across a 50-fold sparsification range, even as the underlying spectrum transitions from Gaussian-unitary-ensemble to sub-Poisson statistics. A 1,200-instance sweep over the inter-system coupling mu confirms that the signal is controlled by mu alone, with no dependence on internal chaos. We further verify that the thermofield double state retains its thermal structure under sparsification despite substantial changes to the state vector, providing a structural explanation for the invariance. These results indicate that the transmission signal diagnoses inter-system coupling fidelity rather than holographic dynamics, and that future quantum-simulation experiments require independent chaos diagnostics to substantiate gravitational claims. As a practical consequence, the invariance implies that 98% of the Hamiltonian's coupling terms can be discarded (with variance rescaling of the survivors), reducing the gate count per Trotter step by approximately 50x at N=10 and bringing larger traversable-wormhole simulations within experimental reach.