  A large number of studies in cognitive science have revealed that
probabilistic outcomes of certain human decisions do not agree with the axioms
of classical probability theory. The field of Quantum Cognition provides an
alternative probabilistic model to explain such paradoxical findings. It posits
that cognitive systems have an underlying quantum-like structure, especially in
decision-making under uncertainty. In this paper, we hypothesise that relevance
judgement, being a multidimensional, cognitive concept, can be used to probe
the quantum-like structure for modelling users' cognitive states in information
seeking. Extending from an experiment protocol inspired by the Stern-Gerlach
experiment in Quantum Physics, we design a crowd-sourced user study to show
violation of the Kolmogorovian probability axioms as a proof of the
quantum-like structure, and provide a comparison between a quantum
probabilistic model and a Bayesian model for predictions of relevance.
