Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness

@article{Hyer2002QuantumCO,
  title={Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness 

},
  author={Peter H{\o}yer and Jan Neerbek and Yaoyun Shi},
  journal={Algorithmica},
  year={2002},
  volume={34},
  pages={429-448}
}
Abstract. We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of (1/π )(ln(N )-1) accesses to the list elements for ordered searching, a lower bound of Ω(N logN ) binary comparisons for sorting, and a lower bound of $\Omega(\sqrt{N}\log{N})$ binary comparisons for element distinctness… 

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