Abstract: Hidden quantum Markovian models are generalizations of classical ones, where the space of of classical states one uses quantum states. This topic can have many applications, e.g. improvement a DNA analysis when quantum effects may play role. The idea is nevertheless new, hence we will discuss only basic results about structure of these models and their consistency as such - nothing of that type is known so far. In the second part we will discuss the question whether a quantum measurement can predict what a person will do in the future. We can present a proof it cannot based on the assumption of a unique unitary evolution.