According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point of this principle is the separation of the document set into two subsets with a given level of fallout and with the highest recall. If subsets of set measures are replaced by subspaces and space measures, we obtain an alternative theory stemming from Quantum Theory. That theory is named after vector probability because vectors represent event like sets do in classical probability. The paper shows that the separation into vector subspaces is more effective than the separation into subsets with the same available evidence. The result is proved mathematically and verified experimentally. In general, the paper suggests that quantum theory is not only a source of rhetoric inspiration, but is a sufficient condition to improve retrieval effectiveness in a principled way.