A quantum no-reflection theorem and the speeding up of Grover's search algorithm

TL;DR

This paper proves a fundamental limit on quantum machines that reflect about unknown states and links this to the optimality of Grover's search, showing that such machines could otherwise exponentially speed up search algorithms.

Contribution

It establishes a no-reflection theorem for unknown states and connects this to the optimality of Grover's algorithm, highlighting fundamental quantum limits.

Findings

Proves the impossibility of universal quantum reflection machines for unknown states

Shows that such machines would enable exponential speedups in Grover's search

Links the no-reflection theorem to the optimality of Grover's algorithm

Abstract

We prove that it is impossible to built a universal quantum machine that produces reflections about an unknown state. We then point out a connection between this result and the optimality of Grover's search algorithm: if such reflection machines were available, it would be possible to accelerate Grover's search algorithm to exponential speedups.