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The pattern matrix method for lower bounds on quantum communication
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Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Two-source extractors secure against quantum adversaries
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On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
Limitations on quantum dimensionality reduction
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The communication complexity of non-signaling distributions
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A lower bound on entanglement-assisted quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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.