We present relation problems whose input size is $n$ such that they can be solved with no communication for entanglement-assisted quantum communication models, but require $Ω(n)$ qubit communication for $2$-way quantum communication models without prior shared entanglement. This is the maximum separation of quantum communication complexity with and without shared entanglement. To our knowledge, our result even shows the first lower bound on quantum communication complexity without shared entanglement when the upper bound of entanglement-assisted quantum communication models is zero. Our result refutes a quantum analog of Newman's theorem. The problem we consider is parallel repetition of any non-local game which has a perfect quantum strategy and no perfect classical strategy, and for which a parallel repetition theorem holds with exponential decay.

翻译：我们提出输入规模为$n$的关系问题，这些问题在纠缠辅助量子通信模型中无需通信即可求解，但在无预先共享纠缠的双向量子通信模型中需要$Ω(n)$量子比特的通信量。这是量子通信复杂性在有/无共享纠缠情形下的最大分离。据我们所知，我们的结果甚至首次给出了当纠缠辅助量子通信模型的上界为零时，无共享纠缠量子通信复杂性的下界。该结果否证了纽曼定理的量子类比。我们所考虑的问题是任何具有完美量子策略但无完美经典策略的非局部博弈的并行重复，且此类博弈满足指数衰减的并行重复定理。