Quantum vs. classical communication and computation
Harry Buhrman, Richard Cleve, Avi Wigderson · 1998
AbotractWC present n simple and general simulation technique that transforms any black-box quantum algorithm (6 la Grover's database search nlgorithm) to a quantum communication protocol for a relntcd problem, in a way that fully exploits the quantum parallelism.This allows us to obtain new positive and negative results.The positive results are novel quantum communication protocols thnt nre built from nontrivial quantum algorithms via this simulation, These protocols, combined with (old and new) classical lower bounds, nre shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) hvoparty communication complexity models.In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separntion for the zero-error model.The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model, In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor ia It possible for the OR function itself in the exact case.This dichotomy naturally suggests a study of bounded-depth predicates (Le.those in the polynomial hierarchy) between OR and MAJORITY.We present black-box algorithms that achieve near quadratic speed up for nil such predicates.