Speed-up and entanglement in quantum searching

Abstract

We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states are product states. In pseudo-pure state implementations, the separability of the states involved defines an entanglement boundary in terms of a bound on the purity parameter. Using this bound we investigate the necessity of entanglement in quantum searching for these pseudopure state implementations. If every active molecule involved in the ensemble is 'charged for' then in existing machines speed-up without entanglement is not possible.