Quantum weakly nondeterministic communication complexity

In this paper we study a weak version of quantum nondeterministic communication complexity, in which a classical proof has to be checked with probability one by a quantum protocol. We prove that, in the framework of communication complexity, even this weak version of quantum nondeterminism is strictly stronger than classical nondeterminism. More precisely, we show a separation, for a total function, of quantum weakly nondeterministic and classical nondeterministic communication complexity. This separation is quadratic and shows that classical proofs can be checked more efficiently by quantum protocols than by classical ones.