ABSTRACT
This chapter sketches out quantum mechanics with the added purpose of clarifying further notation and adopted conventions. It presents a with a 'pragmatic' introduction to the theory, and then refers to a hypothetical "user" of the theory as an artefact to elucidate relationships between the formalism and its operational interpretation. Notions related to quantum non-locality and the information content of quantum states, such as entropies and the characterisation of quantum correlations (also known as entanglement), is the subject of the second half of the chapter. Quantum entanglement, which the founding fathers of the theory used to discuss as a "spooky action at distance", has by now acquired a well-established role as a resource for quantum communication, computation and metrology. The chapter also reviews very basic results in this area. A positive but not completely positive map that serves a key role in the characterisation of quantum entanglement is transposition, in any given basis.
