Classical entanglement underpins the invariant propagation of space–time wave packets

Propagation-invariant pulsed beams are generated by introducing appropriate tight correlations in their spatiotemporal spectrum. Such correlations constitute an example of what has been called "classical entanglement," which is a necessary but insufficient requirement for propagation invariance. We demonstrate theoretically and experimentally that a standard measure of entanglement, the Schmidt number, determines the propagation distance under which the wave packets retain their shape. Reduction in this degree of classical entanglement manifests itself in an increased spread in the measured spatiotemporal spectral correlations.