Computational learning theory: survey and selected bibliography
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Communications of the ACM
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Machine Learning
Machine Learning
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On Computation and Communication with Small Bias
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Unbounded-Error Quantum Query Complexity
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The geometry of quantum learning
Quantum Information Processing
Quantum interpolation of polynomilas
Quantum Information & Computation
| Hi-index | 5.23 |
Given a prior probability distribution over a set of possible oracle functions, we define a number of queries to be useless for determining some property of the function if the probability that the function has the property is unchanged after the oracle responds to the queries. A familiar example is the parity of a uniformly random Boolean-valued function over {1,2,...,N}, for which N-1 classical queries are useless. We prove that if 2k classical queries are useless for some oracle problem, then k quantum queries are also useless. For such problems, which include classical threshold secret sharing schemes, our result also gives a new way to obtain a lower bound on the quantum query complexity, even in cases where neither the function nor the property to be determined is Boolean.