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

8 pages, 3 figures

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