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COCO
2000
Springer

Characterization of Non-Deterministic Quantum Query and Quantum Communication Complexity

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Characterization of Non-Deterministic Quantum Query and Quantum Communication Complexity
It is known that the classical and quantum query complexities of a total Boolean function f 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 f is linearly related to the degree of a “non-deterministic” polynomial for f. We also prove a quantum-classical gap of 1 vs. n for non-deterministic query complexity for a total f. In the case of quantum communication complexity there is a (partly undetermined) relation between the complexity of f and the logarithm of the rank of its communication matrix. We show that the non-deterministic quantum communication complexity of f 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.
Ronald de Wolf
Added 02 Aug 2010
Updated 02 Aug 2010
Type Conference
Year 2000
Where COCO
Authors Ronald de Wolf
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