Quantum lower bounds by polynomials
Journal of the ACM (JACM)
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Theoretical Computer Science - Complexity and logic
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Quantum zero-error algorithms cannot be composed
Information Processing Letters
Tensor rank and strong quantum nondeterminism in multiparty communication
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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It is known that the classical and quantum query complexities of a total Boolean function ý are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the non-deterministic quantum query complexity of ý is linearly related to the degree of a 驴non-deterministic驴 polynomial for ý. We also prove a quantum-classical gap of 1 vs. n for non-deterministic query complexity for a total ý. In the case of quantum communication complexity there is a (partly undetermined) relation between the complexity of ý and the logarithm of the rank of its communication matrix. We show that the non-deterministic quantum communication complexity of ý is linearly related to the logarithm of the rank of a non-deterministic version of the communication matrix, and that it can be exponentially smaller than its classical counterpart can.