We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing quantum inform
ation protocols, originally formulated for finite dimensional quantum systems, to infinite dimensional systems described by continuous variables. This is achieved by using non unitary and non-gaussian operators, obtained from the superposition of gaussian gates, together with adaptative manipulations in qubit systems defined in infinite dimensional Hilbert spaces. We describe in details the realization of single and two qubit gates and briefly discuss their implementation in a quantum optical set-up.
We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known variance produc
t tests in the case of Gaussian states. Furthermore, they involve only a pair of quadrature measurements, and will thus should prove extremely useful the experimental identification of entanglement.
