We exhibit a total search problem whose communication complexity in the quantum SMP (simultaneous message passing) model is exponentially smaller than in the classical two-way randomized model. Moreover, the quantum protocol is computationally efficient and its solutions are classically verifiable, that is, the problem lies in the communication analogue of the class TFNP. Our problem is a bipartite version of a query complexity problem recently introduced by Yamakawa and Zhandry (JACM 2024). We prove the classical lower bound using the structure-vs-randomness paradigm for analyzing communication protocols.

翻译：我们展示了一个完全搜索问题，其在量子SMP（同步消息传递）模型中的通信复杂度相对于经典双向随机化模型呈指数级降低。此外，该量子协议计算高效，其解可被经典验证，即该问题属于通信复杂度版本的TFNP类。我们的问题是Yamakawa与Zhandry（JACM 2024）近期提出的查询复杂度问题的二分版本。我们通过分析通信协议的结构性与随机性范式证明了经典下界。