2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121852We provide a simple security proof for prepare & measure quantum key distribution protocols employing noisy processing and one-way postprocessing of the key. This is achieved by showing that the security of such a protocol is equivalent to that of an associated key distribution protocol in which, instead of the usual maximally-entangled states, a more general {\em private state} is distilled. Besides a more general target state, the usual entanglement distillation tools are employed (in particular, Calderbank-Shor-Steane (CSS)-like codes), with the crucial difference that noisy processing allows some phase errors to be left uncorrected without compromising the privacy of the key.4 pages, to appear in Physical Review Letters. Extensively rewritten, with a more detailed discussion of coherent --> iid reductionQuantum Physicstext