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Quantum correlations; quantum probability approach

This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description of entanglement of formation, and PPT states. This work is intended both for physicists interested not only in collection of results but also in the mathematical methods justifying them, and mathematicians looking for an application of quantum probability to concrete new problems of quantum theory.