High-dimensional maximally entangled photon pairs in parametric down-conversion

This is the authors' abstract. We don't add key points for this paper.

Photon pairs generated from spontaneous parametric down-conversion are a well-established method to realize entangled bipartite photonic systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly exploited to engineer high-dimensional entangled quantum states experimentally. For Hilbert spaces with dimension d>2, maximally entangled states (MES) help to improve the capacity and security of quantum communication protocols, among several other promising features. However, the direct generation of MES in well-defined high-dimensional subspaces of the infinite OAM basis has remained a challenge. Here, we formalize how the spatial distribution of the pump beam and the nonlinear profile of the crystal can be utilized to generate MES without additional spatial filtering of OAM modes within a subspace. We illustrate our approach with maximally entangled qutrits (d=3) and ququints (d=5).