Multi-party Quantum Communication Complexity on Composite Boolean-Valued Function

Abstract

The performance of communication complexity depends on the selected computation model. Even on the specific model the quantum communication complexity is not always better than the classical one. This paper investigates the quantum communication complexity based on a multi-party computation model of the composite Boolean-valued function. On this model we design a quantum distributed algorithm to obtain the upper bound of quantum communication complexity. The result shows that the performance gap between quantum and classical communication complexity depends on the infinity order of function domain’s square root and users’ number. In the best situation the performance of the quantum communication complexity wins the quadratic level of advantage than the classical one. And sometimes the classical way is more efficient than the quantum one.