2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157978We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a large class of codes, only privacy has to be checked.Presented at the NATO ARW "Quantum Communication and Security", 10-13 September 2006, Gdansk, Poland; final version to appear in OSID special issueQuantum Physicstext