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2011 26th Annual IEEE Conference on Computational Complexity
On Arthur Merlin Games in Communication Complexity
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove lower bounds for QMA-communication complexity, and show how one can 'transfer' hardness under an analogous measure in the query complexity model to the communication model using Sherstov's pattern matrix method.Combining a result by Vereshchagin and the pattern matrix method we find a partial function with AM-communication complexity O(\log n), PP-communication complexity \Omega(n^{1/3}), and QMA-communication complexity \Omega(n^{1/6}). Hence in the world of communication complexity noninteractive quantum proof systems are not able to efficiently simulate co-nondeterminism or interaction. These results imply that the related questions in Turing machine complexity theory cannot be resolved by 'algebrizing' techniques. Finally we show that in MA-protocols there is an exponential gap between one-way protocols and two-way protocols for a partial function (this refers to the interaction between Alice and Bob). This is in contrast to nondeterministic, AM-, and QMA-protocols, where one-way communication is essentially optimal.
Index Terms:
communication complexity, Arthur Merlin games, quantum proofs
Hartmut Klauck, "On Arthur Merlin Games in Communication Complexity," ccc, pp.189-199, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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