A quantum lower bound for the collision problem

Details A quantum lower bound for the collision problem A quantum lower bound for the collision problem

2003-04-24

arxiv.org/abs/quant-ph/0304162v1

Physics

Quantum Physics

6 pages Extension of work in quant-ph/0112086

Scientific paper

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.

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