An upper bound on the rate of information transfer by Groverʹs oracle

Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately π / 4 N search using a classical oracle, the search complexity is of order N / 2 queries since on average half of the items must be searched. In work preceding Groverʹs, Bennett et al. had shown that no quantum algorithm can solve the search problem in fewer than O ( N ) algorithm has optimal order of complexity. Here, we present an information-theoretic analysis of Groverʹs algorithm and show that the square-root speed-up by Groverʹs algorithm is the best possible by any algorithm using the same quantum oracle.