  Quantum error correction (QEC) is one of the central concepts in quantum
information science and also has wide applications in fundamental physics. The
capacity theorems provide solid foundations of QEC. We here provide a general
and highly applicable form of capacity theorem for both classical and quantum
information, i.e., hybrid information, with assistance of a limited resource of
entanglement in one-shot scenario, which covers broader situations than the
existing ones. Harnessing the wide applicability of the theorem, we show that a
demonstration of QEC by short random quantum circuits is feasible and that QEC
is intrinsic in quantum chaotic systems. Our results bridge the progress in
quantum information theory, near-future quantum technology, and fundamental
physics.
