Question Question:What's the largest gap between classical and quantum communication complexities? Partial functions,relations:exponential. Total functions,two-way: -Largest gap:Q(Disj)=e(Vn),R(Disj)=e(n) -Best bound:R(f)=exp(Q(f)). ·Conjecture:R(f=poly(Q(f⑤)：Question • Question: What’s the largest gap between classical and quantum communication complexities? • Partial functions, relations: exponential. • Total functions, two-way: – Largest gap: Q(Disj) = Θ(√n), R(Disj) = Θ(n). – Best bound: R(f) = exp(Q(f)). • Conjecture: R(f) = poly(Q(f))