Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity

Xiaoming Sun; Marcos Villagra

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arXiv · 1308.2450

Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity

Xiaoming Sun·Marcos Villagra

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Abstract

There are three different types of nondeterminism in quantum communication: i) $\nqp$-communication, ii) $\qma$-communication, and iii) $\qcma$-communication. In this \redout{paper} we show that multiparty $\nqp$-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 $\nqp$-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.

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Xiaoming Sun, Marcos Villagra. 2013-08-18. Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity. https://arxiv.org/abs/1308.2450

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