Abstract
Grover’s quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state of n qubits. It is shown that the optimal time to perform the measurement is independent of namely, it is identical to the optimal time in the original algorithm in which with the same number of marked states, r. The probability of success is obtained in terms of the amplitudes of the state 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.
- Received 27 May 2003
DOI:https://doi.org/10.1103/PhysRevA.68.022326
©2003 American Physical Society