New perspectives in generation and manipulation of hyperentangled states

Quantum states of two photons simultaneously entangled in polarization and linear momentum, namely hyper-entangled or cluster states, allow to operate in a larger Hilbert space, since we can associate four qubits to two photons. We describe how these states are generated, characterized and manipulated by linear optics technique. Some recent results verifying that the ratio between the quantum and classical prediction grows with the size of the Hilbert space are also presented in this work. Finally, we show the efficient realization of a C-NOT gate by using two photon cluster states operating in the one-way model of quantum computation.