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Nonclassicality of Dirac–Pauli quantum states

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Abstract

In classical physics, a joint measurement of two compatible observables on an enlarged system–apparatus state usually implies that the joint statistics of the corresponding specific system observables are always separable. In this paper, we show that, for the quantum states with its density operators composed of the Dirac–Pauli matrices, the joint statistics of these specific system observables are entangled and the data inversion of the joint statistical distribution is negative. This nonclassical property, which can be revealed by an experimental scheme based on the homodyne detection, maybe helps us to understand the nonlocal features of the quantum tests of the Bell type. When we consider these Dirac–Pauli states as \(2\times 2\) bipartite ones, these bipartite states have a nonzero quantum discord although they are separable.

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Notes

  1. According to the definition and the theorem in Refs. [32, 33], this \(2\times 2\) bipartite state in Eq. (27) can be proved a nonzero discord for \(\theta _1\ne 0, \pi /2, \ \pi ,\ 3\pi /2\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China, Project Nos. 11604243 and 11047015, and the Natural Science Foundation of Tianjin, Project No. 16JCQNJC01600.

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Authors and Affiliations

  1. School of Science, Tianjin University of Technology, Tianjin, 300384, China

    Zong-Guo Li, Zhan-Dong Liu, Rui-Xue Zhang & Hong-Guo Li

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  1. Zong-Guo Li
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  2. Zhan-Dong Liu
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Li, ZG., Liu, ZD., Zhang, RX. et al. Nonclassicality of Dirac–Pauli quantum states. Quantum Inf Process 18, 291 (2019). https://doi.org/10.1007/s11128-019-2405-4

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