How to harness high-dimensional temporal entanglement, using limited interferometry setups

High-dimensional entanglement has shown to have significant advantages in quantum communication. It is available in many degrees of freedom and in particular in the time-domain routinely produced in down-conversion (SPDC). While advantageous in the sense that only a single detector channel is needed locally, it is notoriously hard to analyze, especially in an assumption-free manner that is required for quantum key distribution applications. We develop the first complete analysis of high-dimensional entanglement in the polarization-time-domain and show how to efficiently certify relevant density matrix elements and security parameters for Quantum Key Distribution (QKD). In addition to putting past experiments on rigorous footing, we also develop physical noise models and propose a novel setup that can further enhance the noise resistance of free-space quantum communication.