A large number of qubits is generally required to simulate complex quantum systems, to realize quantum algorithms of increasing complexity and to investigate quantum world at a mesoscopic level.

A second strategy consists of encoding more than one qubit in each particle, by exploiting differentdegrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time. Hyperentanglement corresponds exactly to entangle two particles in different DOFs.

The most important experiments dealing with hyperentangled states of two photons are:

- The generation of particular families of high-dimensional multi-qubit quantum states. In fact, by manipulating the hyperentangled states it has been possible to engineer optical sources for 4- and 6-qubit Cluster states [3] and for 4-qubit Phased Dicke states [5]. While the former have been used to implement QI protocols [1,4], by the second type of states it was possible to study the resilience of entanglement to the noise [5].
- The realization of a versatile source for 2-qubit mixed states, obtained by tracing out the path DOF in the 4-qubit HE state. This source has been used to study extremal quantum correlations by using quantum discord [6].
- The first experimental implementation of an optimal protocol for the characterization of a single-qubit noisy channel [7].

- Experimental study of Non-Markovian dynamics based on low-dimensional quantum states (i.e. 3-qubit)
- Development of higher-dimension quantum photon states (up to 8-qubit)
- Miniaturization of the existing bulk experiments by exploiting the quantum integrated circuits.