Multi-photon entanglement and applications in quantum information
b"Since the awareness of entanglement was raised by Einstein, Podolski, Rosen and Schr\\xf6dinger\\nin the beginning of the last century, it took almost 55 years until entanglement entered the\\nlaboratories as a new resource. Meanwhile, entangled states of various quantum systems\\nhave been investigated. Sofar, their biggest variety was observed in photonic qubit systems.\\nThereby, the setups of today's experiments on multi-photon entanglement can all be structured in the following way: They consist of a photon source, a linear optics network by which\\nthe photons are processed and the conditional detection of the photons at the output of the\\nnetwork.\\nIn this thesis, two new linear optics networks are introduced and their application for\\nseveral quantum information tasks is presented. The workhorse of multi-photon quantum\\ninformation, spontaneous parametric down conversion, is used in different configurations to\\nprovide the input states for the networks.\\nThe first network is a new design of a controlled phase gate which is particularly interesting for applications in multi-photon experiments as it constitutes an improvement of\\nformer realizations with respect to stability and reliability. This is explicitly demonstrated\\nby employing the gate in four-photon experiments. In this context, a teleportation and entanglement swapping protocol is performed in which all four Bell states are distinguished by\\nmeans of the phase gate. A similar type of measurement applied to the subsystem parts of\\ntwo copies of a quantum state, allows further the direct estimation of the state's entanglement\\nin terms of its concurrence. Finally, starting from two Bell states, the controlled phase gate is\\napplied for the observation of a four photon cluster state. The analysis of the results focuses\\non measurement based quantum computation, the main usage of cluster states.\\nThe second network, fed with the second order emission of non-collinear type II spontaneous parametric down conversion, constitutes a tunable source of a whole family of states.\\nUp to now the observation of one particular state required one individually tailored setup.\\nWith the network introduced here many different states can be obtained within the same arrangement by tuning a single, easily accessible experimental parameter. These states exhibit\\nmany useful properties and play a central role in several applications of quantum information.\\nHere, they are used for the solution of a four-player quantum Minority game. It is shown that,\\nby employing four-qubit entanglement, the quantum version of the game clearly outperforms\\nits classical counterpart.\\nExperimental data obtained with both networks are utilized to demonstrate a new method\\nfor the experimental discrimination of different multi-partite entangled states. Although\\ntheoretical classifications of four-qubit entangled states exist, sofar there was no experimental\\ntool to easily assign an observed state to the one or the other class. The new tool presented\\nhere is based on operators which are formed by the correlations between local measurement\\nsettings that are typical for the respective quantum state."