  Quantum information scrambling is a process happening during thermalization
in quantum systems and describes the delocalization of quantum information. It
is closely tied to entanglement, a key resource for quantum technologies and an
order parameter for quantum many-body phenomena. We investigate the effect of
dephasing noise on a multi-qubit teleportation protocol that experimentally
validated quantum information scrambling. We find that while scrambling
enhances information distribution, it is highly noise-sensitive, leading to
decreased teleportation fidelity and an increase in the classical mixing of the
quantum state. Using negativity as a mixed-state entanglement measure, we
identify two fundamentally different entanglement-scaling regimes: efficient
entanglement generation under weak dephasing noise, and entanglement
suppression under strong dephasing noise. We show that in the latter, the
teleportation consumes more entanglement than the scrambling is able to create.
Comparison with a SWAP-gate-based teleportation protocol confirms that the
entanglement suppression is a consequence of the scrambling mechanism. Our
findings suggest that the information dynamics during thermalization is
critically affected by dephasing noise, and confirm that in present-day noisy
quantum devices, local information exchange is preferable over long-range
information scrambling.
