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arXiv · 2304.03960

No-Existence Of Generalize Diffusion

David Ponarovsky
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Abstract

We show that given two arbitrary states $\ketψ,\ketϕ$ it is impossible to compute the transformation: $ \ketψ\ketϕ \mapsto \ketψ\left( \mathbb{I} - 2 \ketψ\braψ \right)\ketϕ $ The contradiction of the existence of such operator follows by showing that using it, two players can compute the disjoints of their sets in a single round and $O\left( \sqrt{n} \right)$ communication complexity, which shown by Braverman to be impossible \cite{Braverman}.

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David Ponarovsky. 2023-04-17. No-Existence Of Generalize Diffusion. https://arxiv.org/abs/2304.03960

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