  Quantum entanglement shared between more than two particles is essential to
foundational questions in quantum mechanics, and upcoming quantum information
technologies. So far, up to 14 two-dimensional qubits have been entangled, and
an open question remains if one can also demonstrate entanglement of
higher-dimensional discrete properties of more than two particles. A promising
route is the use of the photon orbital angular momentum (OAM), which enables
implementation of novel quantum information protocols, and the study of
fundamentally new quantum states. To date, only two of such multidimensional
particles have been entangled albeit with ever increasing dimensionality. Here
we use pulsed spontaneous parametric downconversion (SPDC) to produce photon
quadruplets that are entangled in their OAM, or transverse-mode degrees of
freedom; and witness genuine multipartite Dicke-type entanglement. Apart from
addressing foundational questions, this could find applications in quantum
metrology, imaging, and secret sharing.
