Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity
Xiaoming Sun, Marcos Villagra · arXiv (Cornell University) · 2013
There are three different types of nondeterminism in quantum communication: i) $ qp$-communication, ii) $\qma$-communication, and iii) $\qcma$-communication. In this \redout{paper} we show that multiparty $ qp$-communication can be exponentially stronger than $\qcma$-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue that there exists a total function that is hard for $\qcma$-communication and easy for $ qp$-communication. The proof of it involves an application of the pattern tensor method and a new lower bound for polynomial threshold degree. Another important consequence of this result is that nondeterministic rank can be exponentially lower than the discrepancy bound.