Composite Systems

The treatment of open systems by necessity requires dealing with composite systems. In the framework of quantum probability the composition of systems has to be formulated in terms of the tensor product of the Hilbert spaces associated to each single system. This fact determines the kind of correlations arising in quantum mechanics, leading in particular to the emergence of entanglement. We discuss the notion of entanglement in a bipartite setting for pure states, and briefly point to the extension of the definition to mixed states. We address in particular the connection between entanglement and complete positivity of maps.