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Entanglement and Berry Phase in a Parameterized Three-Qubit System

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Abstract

In this paper, we construct a parameterized form of unitary \(\breve {R}_{123}(\theta _{1},\theta _{2},\varphi )\) matrix through the Yang-Baxterization method. Acting such matrix on three-qubit natural basis as a quantum gate, we can obtain a set of entangled states, which possess the same entanglement value depending on the parameters 𝜃 1 and 𝜃 2. Particularly, such entangled states can produce a set of maximally entangled bases Greenberger-Horne-Zeilinger (GHZ) states with respect to 𝜃 1 = 𝜃 2 = π/2. Choosing a useful Hamiltonian, one can study the evolution of the eigenstates and investigate the result of Berry phase. It is not difficult to find that the Berry phase for this new three-qubit system consistent with the solid angle on the Bloch sphere.

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Acknowledgments

This work was supported by the NSF of China (Grant Nos. 11575042 and 11405026), the Plan for Scientific and Technological Development of Jilin Province (Grant No. 20150520083JH), and government of China through CSC (Grant No. 201506625070).

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Authors and Affiliations

  1. School of Physics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Wenyi Shao, Yangyang Du, Qi Yang, Gangcheng Wang, Chunfang Sun & Kang Xue

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  1. Wenyi Shao
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  2. Yangyang Du
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  3. Qi Yang
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  4. Gangcheng Wang
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  5. Chunfang Sun
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  6. Kang Xue
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Correspondence to Kang Xue.

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Shao, W., Du, Y., Yang, Q. et al. Entanglement and Berry Phase in a Parameterized Three-Qubit System. Int J Theor Phys 56, 643–651 (2017). https://doi.org/10.1007/s10773-016-3206-5

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  • DOI: https://doi.org/10.1007/s10773-016-3206-5

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