Approaches Approach 1:Directly simulate a quantum protocol by classical one. [Aaronson]R1(f)=O(m-Q1(f)). ·Approach2:L(⑤≤Q1(⑤≤R1(⑤≤poly(L(f). -[Nayak99;Jain,Z.'09]R1(f)=O(IVC(f)),where lu is the mutual info of any hard distribution u. Note:For the approach 2 to be possibly succeed, the quantum lower bound L(f)has to be polynomially tight for Q1(f).Approaches • Approach 1: Directly simulate a quantum protocol by classical one. – [Aaronson] R1 (f) = O(m∙Q1 (f)). • Approach 2: L(f) ≤ Q1 (f) ≤ R1 (f) ≤ poly(L(f)). – [Nayak99; Jain, Z.’09] R1 (f) = O(Iμ ∙VC(f)), where Iμ is the mutual info of any hard distribution μ. • Note: For the approach 2 to be possibly succeed, the quantum lower bound L(f) has to be polynomially tight for Q1 (f)