No-Existence Of Generalize Diffusion

04/08/2023

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by   David Ponarovsky, et al.

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We show that given two arbitrary states |ψ⟩,|ϕ⟩ it is impossible to compute the transformation: |ψ⟩|ϕ⟩↦|ψ⟩( 𝕀 - 2 |ψ⟩⟨ψ|)|ϕ⟩ 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( √(n)) communication complexity, which shown by Braverman to be impossible <cit.>.