  The data processing inequality (DPI) is a fundamental feature of information
theory. Informally it states that you cannot increase the information content
of a quantum system by acting on it with a local physical operation. When the
smooth min-entropy is used as the relevant information measure, then the DPI
follows immediately from the definition of the entropy. The DPI for the von
Neumann entropy is then obtained by specializing the DPI for the smooth
min-entropy by using the quantum asymptotic equipartition property (QAEP). We
provide a new, simplified proof of the QAEP and therefore obtain a
self-contained proof of the DPI for the von Neumann entropy.
