Real representation versus communication complexity Suppose that Alice and Bob communicate to compute a function $f:\{0,1\}^n\times\{0,1\}^n\rightarrow\{0,1\}$. Does the minimal degree of a real polynomial/rational representation of $f$ play a role for upper and/or lower bounds on the deterministic, non-deterministic, randomized or quantum communication complexity of computing $f$?
The minimal degree of a real polynomial representing the parity function of $n$ variables is $n$. However, the deterministic communication complexity is at most $2$ bits.