Quantum Lower Bounds for Collision and Element Distinctness with Small Range

@inproceedings{Ambainis2003QuantumLB,
  title={Quantum Lower Bounds for Collision and Element Distinctness with Small Range},
  author={Andris Ambainis},
  year={2003}
}
We give a general method for proving quantum lower bounds for problems with small range. Namely, we show that, for any symmetric problem defined on functions f : {1, . . . , N} → {1, . . . , M}, its polynomial degree is the same for all M ≥ N . Therefore, if we have a quantum query lower bound for some (possibly, quite large) range M which is shown using polynomials method, we immediately get the same lower bound for all ranges M ≥ N . In particular, we get Ω(N) and Ω(N) quantum lower bounds… CONTINUE READING

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