  The aim of this thesis is to investigate quantum entanglement and quantum
nonlocality of bipartite finite-dimensional systems (bipartite qudits).
Entanglement is one of the most fascinating non-classical features of quantum
theory, and besides its impact on our view of the world, it can be exploited
for applications such as quantum cryptography and quantum computing. (...)
Although entanglement and nonlocality are ordinarily regarded as one and the
same, under close consideration this cannot be taken for granted. The reason
for this is that entanglement is defined by the mathematical structure of a
quantum state in a composite Hilbert space, whereas nonlocality signifies that
the statistical behaviour of a system cannot be described by a local realistic
theory. For the latter it is essential that the correlation probabilities of
such theories obey so-called Bell inequalities, which are violated for certain
quantum states. The main focus of this thesis is on the comparison of both
properties with the objective of understanding their relation. (...) Because of
the fact that the correlation probabilities in general depend on the
measurement settings it is necessary to optimise these in order to reveal
nonlocality. This problem is solved for a particular Bell inequality (CGMLP) by
means of a self-developed numerical search algorithm. The method is then
applied to density matrices of a subspace spanned by the projectors of
maximally entangled two-qudit states. This set of states (...) serves to
visualise and analyse the state space geometrically.
