Title: Better Protocol for XOR Game using Communication Protocol and Nonlocal Boxes,
Abstract: Buhrman showed that an efficient communication protocol implies a reliable
XOR game protocol. This idea rederives Linial and Shraibman's lower bounds of
communication complexity, which was derived by using factorization norms, with
worse constant factor in much more intuitive way. In this work, we improve and
generalize Buhrman's idea, and obtain a class of lower bounds for classical
communication complexity including an exact Linial and Shraibman's lower bound
as a special case. In the proof, we explicitly construct a protocol for XOR
game from a classical communication protocol by using a concept of nonlocal
boxes and Paw{\l}owski et al.'s elegant protocol, which was used for showing
the violation of information causality in superquantum theories.