Multi-particle Correlations and Characteristic Bell Inequalities

The correlations between local measurement results are characteristic for multi-partite quantum systems. Under the condition of local realism, which assumes that properties of physical systems exist independent of being measured, and that space-like separated actions on the system cannot influence each other, these correlations are constrained by Bell-inequalities. Quantum mechanics predicts correlations which are not explainable under these two assumptions. The resulting violation of Bell inequalities was originally studied for pairs of entangled particles (Einstein et al.,1935). Meanwhile these ideas were extended to three-and more partite quantum states in particular with respect to the different kinds of multi-particle entanglement and their implications on the obtainable correlations (Mermin, 1990). Here we present a method to construct characteristic Bell inequalities for particular four-qubit states. These inequalities are a versatile tool, not only to provide evidence for non-locality, but also for the characterization of the states, with respect to detection of genuine multipartite entanglement and to state discrimination. Exemplarily we apply our approach to the symmetric four qubit Dicke-state (Dicke, 1954) with two excitations. (A symmetric N-qubit Dicke state with M excitations is the equal superposition of N-qubit pure product states having M logical 1 's and (N-M) logical 0's.) Experimentally the state was observed with photons as carrier of the qubits, using polarization encoding.