Speed-up and entanglement in quantum searching

Speed-up and entanglement in quantum searching

Pati, A.K. and Braunstein, S.L.
(2002): Quantum Information and Computation 2, 399-409. (PDF)

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 pseudo-pure state implementations. If every active molecule involved in the ensemble is `charged for' then in existing machines speed-up without entanglement is not possible.