Entanglement of the orbital angular momentum states of photons

Entangled quantum states are not separable, regardless of the spatial separ ation of their components. This is a manifestation of an aspect of quantum mechanics known as quantum nonlocality(1,2). An important consequence of th is is that the measurement of the state of one particle in a two-particle e ntangled state defines the state of the second particle instantaneously, wh ereas neither particle possesses its own well-defined state before the meas urement. Experimental realizations of entanglement have hitherto been restr icted to two-state quantum systems(3-6), involving, for example, the two or thogonal polarization states of photons. Here we demonstrate entanglement i nvolving the spatial modes of the electromagnetic field carrying orbital an gular momentum. As these modes can be used to define an infinitely dimensio nal discrete Hilbert space, this approach provides a practical route to ent anglement that involves many orthogonal quantum states, rather than just tw o Multi-dimensional entangled states could be of considerable importance in the field of quantum information(7,8), enabling, for example, more efficie nt use of communication channels in quantum cryptography(9-11).