Two theorems of Jhon Bell and Communication Complexity

John Bell taught us that quantum mechanics can not be reproduced by noncontextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area. Introduction Quantum mechanics is a mathematical theory to describe the physical world and at the same time it is a probabilistic theory. But this is not surprising. What is surprising, if we take Copenhagen interpretation for granted, is that this probability is not the probability of some dynamical variable having a particular value in some state, but that represents probability of finding a particular value if that dynamical variable is measured. This interpretation generated numerous debates and following