  Quantum information theory is a very young area of research offering a lot of
challenging open questions to be tackled by ambitious upcoming physicists. One
such problem is addressed in this thesis. Recently, several protocols have
emerged which exploit both continuous variables and discrete variables. On the
one hand, outperforming many of the established pure continuous variable or
discrete variable schemes, these hybrid approaches offer new opportunities.
However, on the other hand, they also lead to new, intricate, as yet
uninvestigated, phenomena.
  An important ingredient of several of these hybrid protocols is a new kind of
entanglement: The hybrid entanglement between continuous variable and discrete
variable quantum systems, which is studied in detail in this work. An
exhaustive analysis of this kind of entanglement is performed, where the focus
is on bipartite entanglement. Nevertheless, also issues regarding multipartite
hybrid entanglement are briefly discussed. The quintessence of this thesis is a
new classification scheme which distinguishes between effective discrete
variable hybrid entanglement and so-called true hybrid entanglement. However,
along the way, also other questions are addressed, which have emerged during
the studies. For example, entanglement witnessing is discussed not only for
hybrid entangled states, but also for fully continuous variable two-mode
Schroedinger cat states. Furthermore, subtleties regarding entanglement
witnessing in a certain kind of mixed states are examined. Not only theoretical
classification and analysis of hybrid entangled states are discussed, but also
their generation is presented and a few applications are demonstrated.
