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Extended Bell inequality and maximum violation |
| Yan Gu(古燕)1, Haifeng Zhang(张海峰)1, Zhigang Song(宋志刚)1, Jiuqing Liang(梁九卿)1, Lianfu Wei(韦联福)2,3 |
1 Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China;
2 State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China;
3 Quantum Optoelectronics Laboratory, School of Physics and Technology, Southwest Jiaotong University, Chengdu 610031, China |
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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 PB is always less than or at most equal to one for the local realistic model (PBlc ≤ 1) regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as PBmax=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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Received: 17 July 2018
Revised: 02 August 2018
Accepted manuscript online:
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PACS:
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03.65.Ud
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(Entanglement and quantum nonlocality)
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03.67.Lx
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(Quantum computation architectures and implementations)
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03.67.Mn
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(Entanglement measures, witnesses, and other characterizations)
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42.50.Dv
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(Quantum state engineering and measurements)
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| Fund: Project supported in part by the National Natural Science Foundation of China (Grant Nos. 11275118 and U1330201). |
Corresponding Authors:
Jiuqing Liang
E-mail: jqliang@sxu.edu.cn
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Cite this article:
Yan Gu(古燕), Haifeng Zhang(张海峰), Zhigang Song(宋志刚), Jiuqing Liang(梁九卿), Lianfu Wei(韦联福) Extended Bell inequality and maximum violation 2018 Chin. Phys. B 27 100303
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