We consider a quantum and classical version multi-party function computation problem with $n$ players, where players $2, \dots, n$ need to communicate appropriate information to player 1, so that a "generalized" inner product function with an appropriate promise can be calculated. The communication complexity of a protocol is the total number of bits that need to be communicated. When $n$ is prime and for our chosen function, we exhibit a quantum protocol (with complexity $(n-1) \log n$ bits) and a classical protocol (with complexity $(n-1)^2 (\log n^2$) bits). In the quantum protocol, the players have access to entangled qudits but the communication is still classical. Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.

翻译：我们考虑一个包含$n$个玩家的量子与经典版本多方函数计算问题，其中玩家$2,\dots,n$需要向玩家1传递适当信息，使得具有特定承诺的“广义”内积函数能够被计算。协议的通信复杂度指需要通信的总比特数。当$n$为素数且针对我们选定的函数时，我们提出一个量子协议（复杂度为$(n-1)\log n$比特）和一个经典协议（复杂度为$(n-1)^2 (\log n^2)$比特）。在量子协议中，玩家能够访问纠缠的量子比特，但通信仍然是经典的。此外，我们提出一个整数线性规划模型用于确定经典通信复杂度的下界，从而证明我们的量子协议严格优于经典协议。