Discrete & Computational Geometry
Fredman-Kolmo´s bounds and information theory
SIAM Journal on Algebraic and Discrete Methods
Better bounds for threshold formulas
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
A lower bound for quantum search of an ordered list
Information Processing Letters
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum Lower Bounds for the Collision and the Element Distinctness Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Better Lower Bound for Quantum Algorithms Searching an Ordered List
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum search of partially ordered sets
Quantum Information & Computation
Hi-index | 0.00 |
Let P = (X, P) be a partial order on a set of n elements X = x1, x2,..., xn. Define the quantum sorting problem QSORTP as: given n distinct numbers x1, x2,..., xn consistent with P, sort them by a quantum decision tree using comparisons of the form "xi: xj". Let Qε(P) be the minimum number of queries used by any quantum decision tree for solving QSORTP with error less than ε (where 0 Algorithmica 34 (2002), 429--448) that, when P0 is the empty partial order, Qε(P0) ≥ Ω (n log n), i. e., the classical information lower bound holds for quantum decision trees when the input permutations are unrestricted.In this paper we show that the classical information lower bound holds, up to an additive linear term, for quantum decision trees for any partial order P. Precisely, we prove Qε(P) ≥ c log2 e(P)-c'n where c,c' 0 are constants and e(P) is the number of linear orderings consistent with P. Our proof builds on an interesting connection between sorting and Korner's graph entropy that was first noted and developed by Kahn and Kim (JCSS 51(1995), 390--399).