A note about claw function with a small range

03/30/2021

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by   Andris Ambainis, et al.

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In the claw detection problem we are given two functions f:D→ R and g:D→ R (|D|=n, |R|=k), and we have to determine if there is exist x,y∈ D such that f(x)=g(y). We show that the quantum query complexity of this problem is between Ω(n^1/2k^1/6) and O(n^1/2+εk^1/4) when 2≤ k<n.