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arXiv · 1807.07236

Extended Bell inequality and maximum violation

Yan Gu·Haifeng Zhang·Zhigang Song·J. -Q. Liang·L. -F. Wei
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Abstract

The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the BI, while the violation is a direct result of the non-local quantum interference between two components of entangled state. The Bell measuring outcome correlation denoted by $P_{B}$ is always less than or at most equal to one for the local realistic model ($P_{B}^{lc}\leq1$) regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as $P_{B}^{\max}$ $=2$, which, however depends on state parameters and three measuring directions as well. Our result is suitable for entangled photon pairs.

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Yan Gu, Haifeng Zhang, Zhigang Song, J. -Q. Liang, L. -F. Wei. 2018-07-19. Extended Bell inequality and maximum violation. https://doi.org/10.1088/1674-1056/27/10/100303

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