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Quantum scissors - finite-dimensional states engineering

This work discusses quantum states defined in a finite-dimensional Hilbert space. In particular, after the presentation of some of them and their basic properties the work concentrates on the group of the quantum optical models that can be referred to as \textit{quantum optical scissors}. Such "devices" can generate on their outputs states that are finite-dimensional, and simultaneously use for such preparation quantum states that are defined in the infinity-dimensional space. The work concentrates on two groups of models: the first one, comprising linear elements and the second one -- models for which optical, Kerr-like nonlinear elements were applied.