Generation of four-dimensional hyperentangled NOON states and beyond with photonic orbital angular momentum and detection-basis control

Abstract

Hyperentanglement of photonic light modes is a valuable resource in quantum information processing and quantum communication. Here we propose a 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 entangled and hyperentangled in at least four dimensions. The resultant state in the four-dimensional case is a generalization of the so-called NOON state (a maximally path-entangled state well known in quantum optics). The production of this state is ``perfect'' (in other words noiseless) 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 a few specific cases to demonstrate the versatility of the system.