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21st Annual IEEE Conference on Computational Complexity (CCC'06) (2006)
Prague, Czech Republic
July 16, 2006 to July 20, 2006
ISSN: 1093-0159
ISBN: 0-7695-2596-2
pp: 288-298
Dmitry Gavinsky , University of Calgary
Julia Kempe , Univ. de Paris-Sud, France
Ronald de Wolf , CWI, Amsterdam
We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomnessSMP protocols by means of quantum SMP protocols without shared randomness (Q^\\-protocols). Our first result is to extend Yao?s simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by Q^\\-protocols. We apply our technique to obtain an efficient Q^\\-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.

J. Kempe, R. de Wolf and D. Gavinsky, "Strengths and Weaknesses of Quantum Fingerprinting," 21st Annual IEEE Conference on Computational Complexity (CCC'06)(CCC), Prague, Czech Republic, 2006, pp. 288-298.
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