  Grover's quantum search algorithm is analyzed for the case in which the
initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is
shown that the optimal time to perform the measurement is independent of $|
\phi>$, namely, it is identical to the optimal time in the original algorithm
in which $| \phi > = | 0>$, with the same number of marked states, $r$. The
probability of success $P_{\rm s}$ is obtained, in terms of the amplitudes of
the state $| \phi>$, and is shown to be independent of $r$. A class of states,
which includes fixed points and cycles of the Grover iteration operator is
identified. The relevance of these results in the context of using the success
probability as an entanglement measure is discussed. In particular, the
Groverian entanglement measure, previously limited to a single marked state, is
generalized to the case of several marked states.
