On the tightness of the buhrman-cleve-wigderson simulation

Abstract

Buhrman, Cleve and Wigderson gave a general communication protocol for block-composed functions by simulating a decision tree computation for f [3]. It is also well-known that this simulation can be very inefficient for some functions f and (g 1, ⋯, g n ). In this paper we show that the simulation is actually polynomially tight up to the choice of (g 1, ⋯, g n ). This also implies that the classical and quantum communication complexities of certain block-composed functions are polynomially related. © 2009 Springer-Verlag Berlin Heidelberg.