  We compare the roles of fidelity and entanglement in characterizing
renormalization group flows and quantum phase transitions. It turns out that
the scaling parameter extracted from fidelity for different ground states
succeeds to capture nontrivial information including stable and unstable fixed
points, whereas the von Neumann entropy as a bipartite entanglement measure (or
equivalently, majorization relations satisfied by the spectra of the reduced
density matrix along renormalization group flows) often fails, as far as the
intrinsic irreversibility-information loss along renormalization group flows-is
concerned. We also clarify an intimate connection between the von Neumman
entropy, majorization relations, and fidelity. The relevance to Zamolodchikov's
c theorem is indicated.
