  Quantum entanglement entropy has a geometric character. This is illustrated
by the interpretation of Rindler space or black hole entropy as entanglement
entropy. In general, one can define a "geometric entropy", associated with an
event horizon as a boundary that concentrates a large number of quantum states.
This allows one to connect with the "density matrix renormalization group" and
to unveil its connection with the theory of quantum information. This
renormalization group has been introduced in condensed matter physics in a
heuristic manner, but it can be conceived as a method of compression of quantum
information in the presence of a horizon. We propose generalizations to
problems of interest in cosmology.
