Lower bounds on the Deterministic and Quantum Communication Complexity of HAM n a
Andris Ambainis, William I. Gasarch, Aravind Srinivasan, Andrey Utis · 2004
Alice and Bob want to know if two strings of length n are almost equal. That is, do theydiffer on at most a bits? Let 0 < = a < = n- 1. We show that any deterministic protocol, as wellas any error-free quantum protocol ( C * version), for this problem requires at least n- 2 bits ofcommunication. We show the same bounds for the problem of determining if two strings differ in exactly a bits. We also prove a lower bound of n/2- 1 for error-free Q * quantum protocols.Our results are obtained by lower-bounding the ranks of the appropriate matrices.