  Electromagnetic pulses are typically treated as space-time (or
space-frequency) separable solutions of Maxwell's equations, where spatial and
temporal (spectral) dependence can be treated separately. In contrast to this
traditional viewpoint, recent advances in structured light and topological
optics have highlighted the non-trivial wave-matter interactions of pulses with
complex topology and space-time non-separable structure, as well as their
potential for energy and information transfer. A characteristic example of such
a pulse is the "Flying Doughnut" (FD), a space-time non-separable toroidal
few-cycle pulse with links to toroidal and non-radiating (anapole) excitations
in matter. Here, we propose a quantum-mechanics-inspired methodology for the
characterization of space-time non-separability in structured pulses. In
analogy to the non-separability of entangled quantum systems, we introduce the
concept of space-spectrum entangled states to describe the space-time
non-separability of classical electromagnetic pulses and develop a method to
reconstruct the corresponding density matrix by state tomography. We apply our
method to the FD pulse and obtain the corresponding fidelity, concurrence, and
entanglement of formation. We demonstrate that such properties dug out from
quantum mechanics quantitatively characterize the evolution of the general
spatiotemporal structured pulse upon propagation.
