  Hyperentanglement of photonic light modes is a valuable resource in quantum
information processing and quantum communication. Here we propose a new
protocol using the interference of two optical nonlinearities and control of
the heralding (detection) basis in the orbital-angular-momentum degree of
freedom. This setup is capable of generating states which are both maximally-
and hyper- entangled in at least four dimensions. The resultant state in the
four-dimensional case is a generalization of the so-called N00N state (a
maximally path-entangled state well known in quantum optics). The production of
this state is "perfect" (in other words noise-less) at least in the ideal case,
excluding experimental imperfections. The presented setup is very versatile,
and with control of the detection and pumping protocols a massively-large
parameter space, of arbitrarily-large dimensionality, may be searched for other
states of interest. Also, we present specific cases demonstrating how the state
may be tuned from two, to three, to four dimensions -- which may be of further
theoretical and experimental interest.
