  High-dimensional entanglement offers promising perspectives in quantum
information science. In practice, however, the main challenge is to devise
efficient methods to characterize high-dimensional entanglement, based on the
available experimental data which is usually rather limited. Here we report the
characterization and certification of high-dimensional entanglement in photon
pairs, encoded in temporal modes. Building upon recently developed theoretical
methods, we certify an entanglement of formation of 2.09(7) ebits in a time-bin
implementation, and 4.1(1) ebits in an energy-time implementation. These
results are based on very limited sets of local measurements, which illustrates
the practical relevance of these methods.
