2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219660We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability bound represents an unique and continuous transition between macroscopic and microscopic measurement precisions.3 pages, 1 figure, completely revised, content unchangedQuantum Physicstext