Causality, Joint measurement and Tsirelson's bound

Abstract

Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality which has been derived under the assumption of existence of joint measurement and no signalling condition.