This proceedings volume contains a broad and representative selection of papers on subjects ranging from Quantum Control, Statistics and Probability, to Operator Algebras and Non-commutative Analysis. The unifying paradigm is the further integration between well established classical fields such as Information Theory, Filtering and Control, Statistical Inference, and their quantum counterparts, using the language of Hilbert space operators and the probabilistic interpretation of quantum mechanics. This synthesis is catalysed by recent developments and promising applications in Quantum Engineering.