  Vector beams (VBs) are fully polarized beams with spatially varying
polarization distributions, and they have found widespread use in numerous
applications such as microscopy, metrology, optical trapping, nano-photonics,
and communications. The entanglement of such beams has attracted significant
interest, and it has been shown to have tremendous potential in expanding
existing applications and enabling new ones. However, due to the complex
spatially varying polarization structure of entangled VBs (EVBs), a complete
entanglement characterization of these beams remains challenging and
time-consuming. Here, we have used a time-tagging event camera to demonstrate
the ability to simultaneously characterize approximately $2.6\times10^6$ modes
between a bi-partite EVB using only 16 measurements. This achievement is an
important milestone in high-dimensional entanglement characterization of
structured light, and it could significantly impact the implementation of
related quantum technologies. The potential applications of this technique are
extensive, and it could pave the way for advancements in quantum communication,
quantum imaging, and other areas where structured entangled photons play a
crucial role.
