2011 IEEE 26th Annual Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 189-199

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.33

ABSTRACT

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

CITATION

H. Klauck, "On Arthur Merlin Games in Communication Complexity,"

*2011 IEEE 26th Annual Conference on Computational Complexity(CCC)*, San Jose, California USA, 2011, pp. 189-199.

doi:10.1109/CCC.2011.33

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