A quantum lower bound for the collision problem
Abstract
Description
We extend Shi's 2002 quantum lower bound for collision in $r$-to-one functions with $n$ inputs. Shi's bound of $Ω((n/r)^{1/3})$ 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.
6 pages Extension of work in quant-ph/0112086
6 pages Extension of work in quant-ph/0112086