Physics – Quantum Physics
Scientific paper
2003-04-24
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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