Query-to-Communication Lifting for BPP

For any n-bit boolean function f, we show that the randomized communication complexity of the composed function f o 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.