  Absorption covers the physical processes which convert intense photon flux
into energetic particles when a high-power laser illuminates optically-thick
matter. It underpins important petawatt-scale applications today, e.g.,
medical-quality proton beam production. However, development of
ultra-high-field applications has been hindered since no study so far has
described absorption throughout the entire transition from the classical to the
quantum electrodynamical (QED) regime of plasma physics. Here we present a
model of absorption that holds over an unprecedented six orders-of-magnitude in
optical intensity and lays the groundwork for QED applications of laser-driven
particle beams. We demonstrate 58% efficient \gamma-ray production at
$1.8\times 10^{25}~\mathrm{W~ cm^{-2}}$ and the creation of an anti-matter
source achieving $4\times 10^{24}\ \mathrm{positrons}\ \mathrm{cm^{-3}}$,
$10^{6}~\times$ denser than of any known photonic scheme. These results will
find applications in scaled laboratory probes of black hole and pulsar winds,
\gamma-ray radiography for materials science and homeland security, and
fundamental nuclear physics.
