## High brilliance source of entangled photon pairs

The realization of a new scheme for generating polarization-entangled photon pairs represents one of the most interesting achievements of the ATESIT project. The high brilliance source realized in the Laboratory of Rome consists of a type-I crystal which operates in an interferometric scheme where all the photon couples emitted at a certain wavelength and belonging to the phase matching cone take part in the entanglement and can be measured. The source is given by a single arm interferometer operating with a Type-I NL crystal, which is excited in two opposite directions by a back-reflected UV pump beam. The generation of a 2-photon linear polarization entangled beam is given by the quantum superposition of the states created by Spontaneous Parametric Down Conversion (SPDC) in the opposite directions k and - k, the last one after back-reflection and suitable phase and polarization transformations. A 213- Bell's inequalities violation was obtained in this configuration and the characteristics of brightness and robustness of the source were confirmed by the fact that more than Ü 106 entangled photon pairs per second are generated by this source with 100mW pump power. This source represents the ideal solution to generate in principle any kind of entangled mixed state with tunable degrees of entanglement and mixedness. Moreover, tunable non maximally entangled states are easily produced by this source without postselection.

Nonlocality tests performed with this source may have a particular significance regarding the possible collection of the whole set of entangled photon pairs belonging to the phase matching cone. Besides Bell�s inequalities, it was possible to give the first experimental demonstration of the Hardy�s ladder proof for a large number of logical steps of the theorem. Testing a large number of steps implies a critical handling of increasingly large statistical samples with rapidly increasing exactness. Experimentally, this requires a high-stability, high-brilliance SPDC source able to generate entangled photon pairs with a high quantum efficiency. The peculiar properties featured by the high brilliance source allowed the substantial accomplishment of such endeavor.

Precisely by the recursive test of 20 ladder's steps a fraction as large as 41% of entangled photon pairs giving a contradiction with local realism was attained. By this source the properties of several relevant families of entangled mixed states can be generated and investigated, as said. Consistently with the above considerations, a patchwork technique, consisting of a sequence of different local operations, has been applied to the realization of the Werner states and the maximally entangled mixed states (MEMS), with variable mixing parameters. These states have been fully characterized by quantum tomography and their non local properties have been also tested. An interesting example of the fruitful joint collaboration of Partner 1 with Partner 3, based on the use of this source, was the first experiment of entanglement detection based on the measurement of an entanglement witness, which is achieved with a minimal number of local measurement settings. Polarized photons in Werner states have been used to perform this test, with perfect agreement with the theoretical predictions.

Finally, by taking advantage of its peculiar spatial characteristics and flexibility in terms of state generation, two photon states simultaneously entangled in polarization and linear momentum (hyper-entangled states), have been produced by the same system. Besides polarization entanglement, momentum entanglement is realized with high phase stability by selecting two symmetric pairs of correlated directions within the conical emission of the type I crystal adopted to generate the parametric fluorescence. The importance of these states in quantum information (QI) resides on the fact that they represent a way to overcome the intrinsic limit of SPDC where no more than one photon pair is created time by time within each microscopic annihilation-creation process. Some QI tasks can be realized by using these states. As an example, in the case of hyper-entangled states, the complete analysis of the four orthogonal Bell states with 100\% efficiency, a result otherwise impossible to achieve with standard linear optics, represents a fundamental tool for many QI objectives. Partner 1, in collaboration with Partner 3, investigated an experimental method to engineer arbitrary pure states of qu-dits, namely d-level quantum systems, i.e. qutrits (d = 3) and ququads (d = 4), using a single nonlinear crystal and linear optical devices as phase waveplates. Hyper-entangled states have been completely characterized in the laboratory of Rome and recently the nonlocal behaviour of these states has been verified by an 'all versus nothing' test of local realism, which represents a generalization of the GHZ to the case of two entangled particles and two observers.

Nonlocality tests performed with this source may have a particular significance regarding the possible collection of the whole set of entangled photon pairs belonging to the phase matching cone. Besides Bell�s inequalities, it was possible to give the first experimental demonstration of the Hardy�s ladder proof for a large number of logical steps of the theorem. Testing a large number of steps implies a critical handling of increasingly large statistical samples with rapidly increasing exactness. Experimentally, this requires a high-stability, high-brilliance SPDC source able to generate entangled photon pairs with a high quantum efficiency. The peculiar properties featured by the high brilliance source allowed the substantial accomplishment of such endeavor.

Precisely by the recursive test of 20 ladder's steps a fraction as large as 41% of entangled photon pairs giving a contradiction with local realism was attained. By this source the properties of several relevant families of entangled mixed states can be generated and investigated, as said. Consistently with the above considerations, a patchwork technique, consisting of a sequence of different local operations, has been applied to the realization of the Werner states and the maximally entangled mixed states (MEMS), with variable mixing parameters. These states have been fully characterized by quantum tomography and their non local properties have been also tested. An interesting example of the fruitful joint collaboration of Partner 1 with Partner 3, based on the use of this source, was the first experiment of entanglement detection based on the measurement of an entanglement witness, which is achieved with a minimal number of local measurement settings. Polarized photons in Werner states have been used to perform this test, with perfect agreement with the theoretical predictions.

Finally, by taking advantage of its peculiar spatial characteristics and flexibility in terms of state generation, two photon states simultaneously entangled in polarization and linear momentum (hyper-entangled states), have been produced by the same system. Besides polarization entanglement, momentum entanglement is realized with high phase stability by selecting two symmetric pairs of correlated directions within the conical emission of the type I crystal adopted to generate the parametric fluorescence. The importance of these states in quantum information (QI) resides on the fact that they represent a way to overcome the intrinsic limit of SPDC where no more than one photon pair is created time by time within each microscopic annihilation-creation process. Some QI tasks can be realized by using these states. As an example, in the case of hyper-entangled states, the complete analysis of the four orthogonal Bell states with 100\% efficiency, a result otherwise impossible to achieve with standard linear optics, represents a fundamental tool for many QI objectives. Partner 1, in collaboration with Partner 3, investigated an experimental method to engineer arbitrary pure states of qu-dits, namely d-level quantum systems, i.e. qutrits (d = 3) and ququads (d = 4), using a single nonlinear crystal and linear optical devices as phase waveplates. Hyper-entangled states have been completely characterized in the laboratory of Rome and recently the nonlocal behaviour of these states has been verified by an 'all versus nothing' test of local realism, which represents a generalization of the GHZ to the case of two entangled particles and two observers.