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：我们考虑一个涉及$n$个参与者的量子与经典版本的多方函数计算问题，其中参与者$2, \dots, n$需要将适当信息传递给参与者1，以便在给定适当承诺的条件下计算一个“广义”内积函数。协议的通信复杂性是指需要通信的总比特数。对于素数$n$以及我们所选的函数，我们展示了一个量子协议（复杂性为$(n-1) \log n$比特）和一个经典协议（复杂性为$(n-1)^2 (\log n^2$比特）。在量子协议中，参与者可以访问纠缠的量子比特，但通信仍然是经典的。此外，我们提出了一种整数线性规划公式，用于确定经典通信复杂性的下界。这表明我们的量子协议严格优于经典协议。