Zia, DanilloDehghan, NazaninD'Errico, AlessioSciarrino, FabioKarimi, Ebrahim2023-09-252023-09-252023Zia, D., Dehghan, N., D’Errico, A. et al. Interferometric imaging of amplitude and phase of spatial biphoton states. Nat. Photon. (2023). https://doi.org/10.1038/s41566-023-01272-3ISSN 1749-4893 (online); ISSN 1749-4885 (print)https://www.nature.com/articles/s41566-023-01272-3http://hdl.handle.net/10393/45462https://doi.org/10.20381/ruor-29668High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterizing these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted; however, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelizing multiple measurements. Here we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference state is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (three orders of magnitude faster) and reliable (an average fidelity of 87%) characterization of states in arbitrary spatial modes bases, compared with previously performed experiments. Multiphoton digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Articlehttps://doi.org/10.1038/s41566-023-01272-3