Is entanglement an exclusive feature of quantum systems, or is it common to
all non-classical theories? And if this is the case, how strong is quantum
mechanical entanglement as compared to that exhibited by other theories? The
first part of this thesis deals with these questions by considering quantum
theory as part of a wider landscape of physical theories, collectively called
general probabilistic theories (GPTs). Among the other things, this manuscript
contains a detailed introduction to the abstract state space formalism for
GPTs. We start with a comprehensive review of the proof of a famous theorem by
Ludwig that constitutes one of its cornerstones (Ch. 1). After explaining the
basic rules of the game, we translate our questions into precise conjectures
and present our progress toward a full solution (Ch. 2). In Ch. 3 we consider
entanglement at the level of measurements instead of states, focusing on one of
its main implications, i.e. data hiding. We determine the maximal data hiding
strength that a quantum mechanical system can exhibit, and also the maximum
value among all GPTs, finding that the former scales as the square root of the
latter. In the second part of this manuscript we look into quantum
entanglement. In Ch. 4 we discuss the entanglement transformation properties of
a class of maps that model white noise acting either locally or globally on a
bipartite system. In Ch. 5 we employ matrix analysis tools to develop a unified
approach to Gaussian entanglement. The third part of this thesis concerns more
general forms of non-classical correlations in bipartite continuous variable
systems. In Ch. 6 we devise a general scheme that allows to consistently
classify correlations of bipartite Gaussian states into classical and quantum
ones. Finally, Ch. 7 explores some problems connected with a certain strong
subadditivity matrix inequality.