The Local Search problem, which finds a
local minimum of a black-box function on a given graph, is of both
practical and theoretical importance to many areas in computer
science and natural sciences. In this paper, we show that for the
Boolean hypercube $\B^n$, the randomized query complexity of Local
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A strong direct product theorem (SDPT) states that solving $n$ instances of a problem requires $\Omega(n)$ times the resources for a single instance, even to achieve success probability $2^{-\Omega(n)}.$ We prove that quantum communication complexity obeys an SDPT whenever the communication lower bound for a single instance is proved by ... more >>>