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：广义扩散不存在
翻译摘要:
我们证明不存在一个算子，可以给定两个状态 $|\psi\rangle,|\phi\rangle$ 并计算变换 $D|\psi\rangle|\phi\rangle = |\psi\rangle\bigl( \mathbb{I} - 2 |\psi\rangle\langle\psi| \bigr)|\phi\rangle$。这个矛盾结果由于说明利用 $D$ 两个玩家可以在单轮中以 $O\left( \sqrt{n} \right)$ 的通信复杂度计算它们的异集（disjoint），而 Braverman 已证明这是不可能的 \cite{Braverman}。
注意: 在译文中，专有名词需要用英文标注。
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