  It is shown that the fidelity, a basic notion of quantum information science,
may be used to characterize quantum phase transitions, regardless of what type
of internal order is present in quantum many-body states. If the fidelity of
two given states vanishes, then there are two cases: (1) they are in the same
phase if the distinguishability results from irrelevant local information; or
(2) they are in different phases if the distinguishability results from
relevant long-distance information. The different effects of irrelevant and
relevant information are quantified, which allows us to identify unstable and
stable fixed points (in the sense of renormalization group theory). A physical
implication of our results is the occurrence of the orthogonality catastrophe
near the transition points.
