Basics of Quantum Theory for Quantum-Like Modeling Information Retrieval

This chapter contains a brief introduction to the mathematical formalism and axiomatics of quantum mechanics (QM). Recently quantum mathematics and methodology started to be widely used for modeling decision making for humans and AI-systems, including quantum-like modeling information retrieval. Experts in such areas do not go deeply into the details of quantum theory. Moreover, typically such consumers of quantum theory do not use all its components. Quantum measurement theory is the most useful for application, including information retrieval. The main issue is the quantum treatment of incompatible observables represented mathematically by noncommuting Hermitian operators. At the level of statistical data incompatibility is represented as interference of probabilities, in the form of modification of the formula of total probability by adding the interference term.

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