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arXiv:1007.4775 · Physics Letters A

Violation of Clauser–Horne–Shimony–Holt inequality for states resulting from entanglement swapping

Antoni Wójcik, Joanna Modławska, Andrzej Grudka, Mikołaj Czechlewski

Published Oct 4, 2010• 21 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2010.09.069

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We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved, then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.
The Bell--Clauser-Horne-Shimony-Holt (BCHSH) inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that nonmaximally entangled states violate the BCHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Ac\'{\i}n et al. [Phys. Rev. A 65,65,65, 052325 (2002)] using the Bell--Clauser-Horne inequality (in terms of probabilities).