On the cognitive experiments to test quantum-like behaviour of mind

We describe cognitive experiments (based on interference of probabilities for mental observables) that could verify quantum-like structure of mental measurements. In principle, such experiments could be performed in psychology, cognitive and social sciences. Recently one of such experiments (described in the previous version of the preprint) based on recognition of images was performed. It confirms our prediction on quantum-like behaviour of mind. The recognition of the exclusive role that averages should play in the theory of mental measurements induces the impression that quantum-like models could be useful to describe mental states. From the beginning we should underline that for us quantum theory is merely a special theory of statistical averages. The main distinguishing feature of quantum theory of averages (compare to classical statistical mechanics) is that here we have the deterministic equation (Schrödinger equation) not for probabilities, but for square roots of probabilities, quantum states. The main experimental consequence of special quantum probabilistic behaviour is the interference of probabilities, see e.g. [1], [2] and see e.g. [3]-[5] for the detailed analysis. In classical statistical physics the probability of the event C = A or B, where A and B are alternatives, is equal to the sum of