Bent, N.Qassim, H.Tahir, A. A.Sych, D.Leuchs, GerdSánchez Soto, Luis LorenzoKarimi, E.Boyd, R. W.2023-06-182023-06-182015-10-152160-330810.1103/PhysRevX.5.041006https://hdl.handle.net/20.500.14352/24259© American Physical Society. The authors thank Markus Grassl and Joseph M. Renes for fruitful discussions. The authors acknowledge the support of the Canada Excellence Research Chairs (CERC) Program. R.W. B. was supported by the DARPA InPho program. L. L. S.-S. acknowledges support from the Spanish MINECO (Grant No. FIS2011-26786) and the Program UCM-BSCH (Grant No. GR3/14).Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81-0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.engjournal articlehttp://dx.doi.org/10.1103/PhysRevX.5.041006http://journals.aps.org/open access535Mutually unbiased basesState determinationAngular-momentumÓptica (Física)2209.19 Óptica Física