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Photon-Pair States and Violation of CHSH Inequality

Pinto, L. M. ; Almeida, A. ; André, P.S ; Pinto, A. N.

Microwave and Optical Tech. Letters Vol. 54, Nº 11, pp. 2454 - 2461, November, 2012.

ISSN (print): 0895-2477
ISSN (online): 0895-2477

Journal Impact Factor: 0,743 (in 2008)

Digital Object Identifier: 10.1002/mop.27127

Abstract
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=2sqrt(2), for the pure entangled
quantum state. Using the spontaneous four-wave mixing (FWM)
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
(GHZ) state and for an arbitrary state of two particles.