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 $1.8times 10^{25}~mathrm{W~ cm^{-2}}$ and the creation of an anti-matter source achieving $4times 10^{24} mathrm{positrons} mathrm{cm^{-3}}$, $10^{6}~times$ 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.
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