Michael Elkin, Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan
We study lower bounds for quantum distributed network computing, where a set of nodes (representing quantum computers) interconnected by an underlying network consisting of (bandwidth-restricted) quantum communication links, communicate using quantum communication. We show non-trivial time lower bounds of quantum distributed algorithms for fundamental graph problems. Our bounds are strong in the sense that they hold even when nodes have unlimited computational power and share an unlimited number of entangled qubits. Our bounds hold for many fundamental graph {\em verification} problems as well as for various graph {\em optimization} problems (both exact and approximate optimization). Our lower bounds are shown in a uniform way by showing a connection between quantum communication complexity and quantum distributed computing and hence gives a general technique for showing lower bounds for a wide variety of distributed network problems in the quantum setting.
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http://arxiv.org/abs/1207.5211
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