Information-theoretic lower bounds for quantum sorting
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We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set P and are asked to identify a linear extension of P using pairwise comparisons. For the standard sorting problem, in which P is empty, it is known that the quantum query complexity is not asymptotically smaller than the classical information-theoretic lower bound. We prove that this holds for a wide class of partially ordered sets, thereby improving on a result from Yao (STOC'04).
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