Algebraic Characterization of Biphoton Spatial-Mode Entanglement in Higher-Order Laguerre--Gaussian-Pumped SPDC
This work develops an algebraic framework to describe spatial-mode entanglement in SPDC generated by higher-order Laguerre-Gaussian (LG) pumps. By factoring the process into a beam splitter and squeezing operator, it reveals how radial and azimuthal pump indices control the dimensionality of the resulting biphoton entanglement, leading to new conservation laws.