We show that there is no operator that given two state $|\psi\rangle,|\phi\rangle$ compute the transformation: $D|\psi\rangle|\phi\rangle = |\psi\rangle\bigl( \mathbb{I} - 2 |\psi\rangle\langle\psi| \bigr)|\phi\rangle$ The contradiction of the existence follows by showing that using $D$ two players can compute the disjoints of their sets in single round and $O\left( \sqrt{n} \right)$ communication complexity, which shown by Braverman to be impossible \cite{Braverman}.

翻译：我们证明不存在这样的算子：给定两个态$|\psi\rangle,|\phi\rangle$，能够计算变换$D|\psi\rangle|\phi\rangle = |\psi\rangle\bigl( \mathbb{I} - 2 |\psi\rangle\langle\psi| \bigr)|\phi\rangle$。存在性的矛盾源于以下论证：利用算子$D$，两个玩家可以在单轮通信中以$O\left( \sqrt{n} \right)$的通信复杂度计算其集合的不交性，而Braverman已证明这是不可能的\cite{Braverman}。