Adversary Lower Bounds for the Collision and the Set Equality Problems

Aleksandrs Belovs; Ansis Rosmanis

Adversary Lower Bounds for the Collision and the Set Equality Problems

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arxiv 1310.5185 v4 pith:ABXS24MV submitted 2013-10-19 quant-ph

Aleksandrs Belovs , Ansis Rosmanis This is my paper · ORCID

classification quant-ph

keywords adversaryboundscollisionequalitylowerproblemsaaronsonalphabet

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abstract

We prove tight $\Omega(n^{1/3})$ lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.

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The Compressed Oracle is a Worthy (Multiplicative) Adversary
quant-ph 2025-09 conditional novelty 6.0 of 10

The compressed oracle technique is captured by the multiplicative adversary method through the new multiplicative ladder adversary method, up to a factor of 6.

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