Orbital angular momentum uncertainty relations of entangled two-photon states

The inseparability of quantum correlation requires that the particles in the composite system be treated as a whole rather than treated separately, a typical example is the Einstein-Podolsky-Rosen (EPR) paradox. In this paper, we provide a theoretical study on the uncertainty relations of two kinds of bipartite observables in two-photon orbital angular momentum (OAM) entanglement, that is, the relative distance and centroid of the two photons at azimuth. We find that the uncertainty relations of the bipartite observables holds in any two-photon state, and they are separable in two-photon OAM entanglement. In addition, the entangled state behaves as a single particle in the bipartite representation. Finally, we find that the uncertainty relations of the bipartite observables can be used to manipulate the degree of the entanglement of an EPR state.