A quantum lower bound for the collision problem

Samuel Kutin

A quantum lower bound for the collision problem

量子物理 2007-05-23 v1

作者: Samuel Kutin

摘要

We extend Shi's 2002 quantum lower bound for collision in $r$ -to-one functions with $n$ inputs. Shi's bound of $\Omega((n/r)^{1/3})$ is tight, but his proof applies only in the case where the range has size at least $3n/2$ . We give a modified version of Shi's argument which removes this restriction.

引用

@article{arxiv.quant-ph/0304162,
  title  = {A quantum lower bound for the collision problem},
  author = {Samuel Kutin},
  journal= {arXiv preprint arXiv:quant-ph/0304162},
  year   = {2007}
}

备注

6 pages Extension of work in quant-ph/0112086

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