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.

• Type: Conference
• Year: 2000
• Where: COCO
• Authors: Ronald de Wolf
• Keywords: Algorithms, COCO 2000, Non-deterministic Quantum, Quantum Communication Complexity, Quantum Query