June 10, 2026 -- Quantum technologies promise revolutionary advances in communication, imaging and sensor technology – yet their potential depends crucially on the quality and controllability of the underlying entanglement. Researchers at the Institute of Applied Physics within the Department of Physics at TU Darmstadt have now published a comprehensive review article on so-called position-momentum entanglement, which summarises the current state of the field and highlights prospects for future applications. The paper appeared in the renowned journal Laser & Photonics Reviews.

The review focuses on a particular form of quantum entanglement: the position-momentum entanglement of photons. It dates back to the famous EPR paradox proposed by Einstein, Podolsky and Rosen in 1935 and describes how two photons can be correlated in such a way that measuring the position or momentum of one photon immediately allows conclusions to be drawn about the other – regardless of their spatial distance. Unlike polarisation entanglement, which is based on a two-dimensional Hilbert space, spatial entanglement provides access to high-dimensional, continuous quantum systems. This increases the information capacity and makes such states more robust against disturbances.

The generation of entangled photon pairs typically occurs via the nonlinear optical process of spontaneous parametric down-conversion (SPDC): a high-energy pump photon is converted into two lower-energy photons – signal and idler – within a nonlinear crystal. Conservation of energy and momentum ensures characteristic correlations in the position and momentum of the generated photons. The group led by Professor Markus Gräfe at the Institute of Applied Physics describes in the review how various crystal parameters, pump beam profiles and phase-matching conditions can be specifically utilised to shape and optimise spatial entanglement.

A versatile and increasingly well-controllable tool for quantum technology

A significant part of the work is devoted to the measurement methods with which entanglement can be detected and quantified – from the estimation of the number of spatial modes via Schmidt decomposition to direct coincidence measurement in near and far fields using highly sensitive cameras. Finally, the authors discuss specific fields of application: from quantum key distribution through quantum imaging and quantum metrology to quantum teleportation. The overview highlights that spatial entanglement represents a versatile and increasingly well-controllable tool for quantum technology.

The study was conducted primarily at the Institute of Applied Physics at TU Darmstadt, with Jorge Fuenzalida as a co-author; he now works at the ICFO-Institut de Ciencies Fotoniques in Barcelona.