  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.
