2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172723The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.12 pages, 2 figures, strongly extended versionQuantum PhysicsHigh Energy Physics - TheoryMathematical Physicstext