Curator's Take
This article tackles a long‑standing bottleneck in high‑dimensional photonic entanglement by finally providing a practical way to access the radial Schmidt modes of SPDC photons, expanding the usable Hilbert space beyond the well‑studied azimuthal and pixel bases. By showing that azimuthal averaging yields a clean radial Schmidt decomposition and demonstrating a density‑matrix reconstruction that resolves up to 50 modes with 98 % fidelity, the work opens the door to richer quantum‑communication protocols and more sensitive quantum imaging schemes that can exploit the full transverse structure of light. The result complements recent advances in mode‑sorting technologies and suggests that future experiments could combine radial and azimuthal degrees of freedom for truly ultra‑high‑dimensional entanglement, though scaling the technique to even larger mode numbers will still require careful control of optical aberrations and detector resolution.
— Mark Eatherly
Summary
High-dimensional spatially entangled two-photon state generated by spontaneous parametric down-conversion process (SPDC) has become a promising resource for several quantum information science applications. For harnessing high-dimensional entanglement advantages, detection capability in the Schmidt basis is a necessity. Spatial entanglement has been explored in several modal bases, such as pixel, azimuthal, and radial modes. Among them, pixel and azimuthal entanglement have been widely utilized due to efficient access to their Schmidt modes, while radial-mode entanglement remains underexploited. This is because for radial coordinates, there is neither a Schmidt-decomposed form for the SPDC photons nor is there a technique for measuring high-dimensional radial Schmidt modes, which is a major roadblock in harnessing radial mode advantages. In this work, we first theoretically show that the azimuthal averaging of SPDC two-photon state yields a radial Schmidt-decomposed form under typical experimental situations. We then demonstrate an innovative approach for extracting the radial Schmidt modes and their spectrum by characterizing the density matrix in the radial basis of one of the SPDC photons. Finally, we report the first-ever measurement of radial Schmidt spectrum of upto 50 radial Schmidt modes with about 98\% fidelity.