Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.

The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 5: Submitted. Paper 6: Submitted.</p>

Dans cette thèse, nous mesurons la dynamique cohérente et les corrélations spatiales des excitations Rydberg dans des matrices 2D d’atomes uniques.Nous utilisons un modulateur spatial de lumière pour façonner la phase spatiale d'un faisceau laser de piégeage optique avant de le focaliser avec une lentille asphérique de grande ouverture numérique. En imprimant une phase appropriée sur le faisceau laser, nous pouvons créer des matrices 2D de pièges optiques, de forme arbitraire et facilement reconfigurables, avec jusqu'à 100 pièges séparées de quelques micromètres. Les pièges sont chargés à partir d'un nuage d'atomes froids de 87Rb, et due aux collisions assistées par la lumière, au plus un seul atome peut être présent dans chaque piège en même temps. Une caméra CCD sensible permet en temps réel l'imagerie de la fluorescence atomique émanant des pièges, ce qui nous permet de détecter individuellement la présence d'un atome dans chaque piège avec une précision presque parfaite.Pour créer des interactions importantes entre les atomes uniques, nous les excitons vers des états de Rydberg, qui sont des états électroniques avec un nombre quantique principal élevé.Un faisceau supplémentaire d'adressage permet la manipulation individuelle d'un atome sélectionné dans la matrice.La connaissance précise, de la fois de la matrice des atomes préparé et des positions des excitations Rydberg, nous a permis de mesurer l’augmentation collective de la couplage optique dans le régime de blocage Rydberg, où une seule excitation est partagée de façon symétrique entre tous les atomes de la matrice.Dans le régime où l'interaction ne s’étend que sur quelques sites, nous avons mesuré la dynamique et les corrélations spatiales des excitations Rydberg, dans des matrices d’atomes à une et deux dimensions. La comparaison à une simulation numérique d'un modèle d'Ising quantique d'un système de spin-1/2 montre un accord exceptionnel pour les matrices où l'effet de l'anisotropie de l’interaction Rydberg-Rydberg est faible. Les résultats obtenus démontrent que les atomes Rydberg uniques sont une plate-forme bien adaptée pour la simulation quantique des systèmes de spin. / In this thesis, we measure the coherent dynamics and the pair correlations of Rydberg excitations in two-dimensional arrays of single atoms.We use a spatial light modulator to shape the spatial phase of a single optical dipole trap beam before focusing it with a high numerical-aperture aspheric lens. By imprinting an appropriate phase pattern on the trap beam, we can create arbitrarily shaped and easily reconfigurable 2D arrays of high-quality single-atom traps, with trap-spacings of a few micrometers for up to 100 traps. The traps are loaded from a cloud of cold 87Rb atoms, and due to fast light-assisted collisions of atoms inside the traps, at most one atom can be present in each trap at the same time. A sensitive CCD camera allows the real-time, site-resolved imaging of the atomic fluorescence from the traps, enabling us to detect the presence of an atom in each individual trap with almost perfect accuracy.In order to induce strong, tunable interactions between the atoms in the array, we coherently laser-excite them to Rydberg states, which are electronic states with a high principal quantum number.An additional addressing beam allows the individual manipulation of an atom at a selected site in the array.The precise knowledge of both the prepared atom array and the positions of the Rydberg excitations allowed us to measure the collective enhancement of the optical coupling strength in the regime of full Rydberg blockade, where one single excitation is shared symmetrically among all atoms in the array.In the regime where the strong interaction only extends over a few sites, we measured the dynamics and the spatial pair-correlations of Rydberg excitations, in one- and two-dimensional atom arrays. The comparison to a numerical simulation of a quantum Ising model of a spin-1/2 system shows an exceptional agreement for trap geometries where the effect of the anisotropy of the Rydberg-Rydberg interaction is small. The obtained results demonstrate that single Rydberg atoms are a suitable platform for the quantum simulation of spin systems.