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Spatially entangled light has proven to be a critical resource in high-dimensional quantum information applications such as quantum cryptography, quantum sensing, and quantum computing. However, progress in the generation of arbitrary spatially entangled states for these protocols via spontaneous parametric down-conversion has been hindered due to the complex relationship between the nonlinear coupling and the generated quantum state. Here, we employ an inverse-design algorithm for the generation of non-trivial maximally entangled bi-photon qubit and qutrit states in the azimuthal index via spontaneous parametric down-conversion. These states are obtained by shaping the pump spatial distribution as a superposition of Laguerre-Gaussian radial modes. The generated bi-photon states are experimentally characterized through quantum state tomography, with their entanglement verified by breaking generalized Bell inequalities. Finally, we performed a proof-of-principle experiment demonstrating the potential utility of the inverse-designed states in entanglement-based quantum key distribution protocols, measuring quantum error rates of 3.95% and 7.03% for the generated qubit and qutrit states, respectively. Our results validate the inverse-design model in a free-space optical setup and pave the way for high-dimensional spatial-mode entangled state design and generation for quantum network applications.
Foley-Comer et al. (Tue,) studied this question.