Improved Separations between Quantum and Classical Communication Complexity of Total Functions

RESUMO

We refine Gavinsky's framework ( arXiv:2608.18784 ) for exponential separations between quantum and randomized communication complexity of total functions and obtain larger separations: polylogarithmic quantum communication versus $\tilde\Omega(\sqrt n)$ randomized communication with two quantum messages, and versus $\Omega(n^{1-\varepsilon})$ for every fixed $0<\varepsilon<1$ with more quantum messages.