This paper demonstrates that how well a state performs as an input to Grover’s search algorithm depends critically upon the entanglement present in that state; the more the entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability $P_{\max }$ that the search algorithm succeeds. We prove that, for pure states, $P_{\max }$ is an entanglement monotone, in the sense that $P_{\max }$ can never be decreased by local operations and classical communication.

• Received 17 December 2001

DOI:https://doi.org/10.1103/PhysRevA.65.062312