2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90343It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is {\em impossible} to do so if the transformation is anti-linear and non-singular. This result implies that unitary and anti-unitary operations exist on an unequal footing in quantum information theory.5 pages, no figuresQuantum Physicstext