Photon‐pair states and violation of CHSH inequality

In addition to Bell's original inequality, John Clauser, Michael Horne, Abner Shimony, and Richard Holt (CHSH) developed a special form of Bell's inequality which gives classical limits to the expected correlation between two particles. We present a theoretical demonstration of the maximum value for violation of CHSH inequality, S = 2 $\sqrt{2}$ , for the pure entangled quantum state. Using the spontaneous four‐wave mixing process, we generate polarization‐entangled photon pairs in a highly nonlinear fiber (HNLF) loop, for experimental verification. Using a nonentangled quantum state, we show theoretically that the violation of CHSH inequality is only a property of entangled states. We also show the theoretical solution of violation of the CHSH inequality for a general Greenberger–Horne–Zeilinger state and for an arbitrary state of two particles. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2454–2461, 2012; View this article online at wileyonlinelibrary. com. DOI 10.1002/mop.27127