  In the last decades, it has been understood that a wide variety of phenomena
in quantum field theory (QFT) can be characterised using quantum information
measures, such as the entanglement entropy of a state and the relative entropy
between quantum states in the same Hilbert space. In this thesis, we use these
and other tools from quantum information theory to study several interesting
problems in quantum field theory. The topics analysed range from the study of
the Aharonov-Bohm effect in QFT using entanglement entropy, to the consistence
of the Ryu-Takayanagi formula (proposed in the context of the AdS/CFT duality)
using properties of relative entropy. We show that relative entropy can also be
used to obtain new interesting quantum energy inequalities, that constrain the
spatial distribution of negative energy density.
