  We define a quantum model for multiparty communication complexity and prove a
simulation theorem between the classical and quantum models. As a result of our
simulation, we show that if the quantum k-party communication complexity of a
function f is $\Omega(n/2^k)$, then its classical k-party communication is
$\Omega(n/2^{k/2})$. Finding such an f would allow us to prove strong classical
lower bounds for (k>log n) players and hence resolve a main open question about
symmetric circuits. Furthermore, we prove that for the Generalized Inner
Product (GIP) function, the quantum model is exponentially more efficient than
the classical one. This provides the first exponential separation for a total
function between any quantum and public coin randomized communication model.
