Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions

Abstract

We establish a mapping between a continuous variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system of arbitrary dimension. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite dimensional Hilbert space and thus can be considered as a universal resource of entanglement. As an explicit example of the formalism a two-mode CV entangled state is mapped onto a two-qutrit entangled state.