  The paper shows that ranking information units by quantum probability differs
from ranking them by classical probability provided the same data used for
parameter estimation. As probability of detection (also known as recall or
power) and probability of false alarm (also known as fallout or size) measure
the quality of ranking, we point out and show that ranking by quantum
probability yields higher probability of detection than ranking by classical
probability provided a given probability of false alarm and the same parameter
estimation data. As quantum probability provided more effective detectors than
classical probability within other domains that data management, we conjecture
that, the system that can implement subspace-based detectors shall be more
effective than a system which implements a set-based detectors, the
effectiveness being calculated as expected recall estimated over the
probability of detection and expected fallout estimated over the probability of
false alarm.
