The observation of the non-local properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work, we investigate the robustness of the non-locality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing non-locality in terms of experimental noise parameters, and demonstrate the importance of the choice of the measurement bases for optimizing the robustness. For W states, in the phase damping case, we show that this choice can lead to a trade-off between obtaining a high violation of the non-local test and optimal robustness thresholds; we also show that in this setting the nonlocality of W states is particularly robust for a large number of qubits. Furthermore, we apply our techniques to the discrimination of symmetric states belonging to different entanglement classes, thus illustrating their usefulness for a wide range of practical quantum information applications.

In this work we present a generalization of the recently developed Hardy-like logical proof of contextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greater than three. Our approach uses compatibility graphs that can only be satisfied by qudits. We find a construction for states and measurements that satisfy these graphs and demonstrate both logical and inequality based contextuality for qudits. Interestingly, the quantum violation of the inequality is constant as dimension increases. We also discuss the issue of imprecision in experimental implementations of contextuality tests and a way of addressing this problem using the notion of ontological faithfulness.