SIAM Journal on Computing, Volume 49, Issue 4, Page FOCS17-441-FOCS17-461, January 2020.
For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In particular, this means that many query complexity separations involving randomized models (e.g., classical vs. quantum) automatically imply analogous separations in communication complexity.

中文翻译：

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BPP的查询到通信提升

SIAM Journal on Computing，第49卷，第4期，第FOCS17-441-FOCS17-461页，2020年1月。
对于任何$ n $位布尔函数$ f $，我们证明了组合函数$ f \的随机通信复杂度。 circ g ^ n $，其中$ g $是索引小工具，其特征在于$ f $的随机决策树复杂度。特别是，这意味着涉及随机模型（例如经典模型与量子模型）的许多查询复杂性分离会自动暗示通信复杂性的类似分离。