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Multipartite strongly symmetric states and applications to geometric entanglement and classicality

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Abstract

Multipartite quantum resources, such as entanglement and coherence, have long been a question of great interest in quantum information science. In this literature, we introduce the concept of multipartite strongly symmetric states that their representation tensors are strongly symmetric tensor. The dimension of strongly symmetric subspace is discussed, and show that is less than the dimension of symmetric subspace. We present some upper bound for the geometric measure of entanglement of strongly symmetric states, which are tighter than the bounds in N-qubit system. On the other hand, we consider the classicality of spin states in strongly symmetric situation, which is equivalent to the positive semidefiniteness of strongly symmetric representation tensor. Some sufficient conditions for classicality (separability) in strongly symmetric case are proposed, and these methods have a larger detection range than the smallest eigenvalue method. In addition, we also present some theoretical upper bounds for quantumness of strongly symmetric states, which are tighter than existing bounds.

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Acknowledgements

Research of Sze was supported by a HK RGC grant PolyU 15300121 and a PolyU research grant 4-ZZRN. The HK RGC grant also supported the post-doctoral fellowship of Xiong at the Hong Kong Polytechnic University. This work was also supported by the National Natural Science Foundation of China (Grant Nos. 11971413, 12175150) and the Guangdong Basic and Applied Basic Foundation (Grant No.2022A1515011995).

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liang Xiong & Nung-sing Sze

  2. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China

    Qi Qin, Zhirui Gong & Zhanfeng Jiang

  3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Jianzhou Liu

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  1. Liang Xiong
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  2. Qi Qin
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  3. Jianzhou Liu
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  4. Zhirui Gong
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  5. Zhanfeng Jiang
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  6. Nung-sing Sze
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Correspondence to Liang Xiong, Zhanfeng Jiang or Nung-sing Sze.

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Xiong, L., Qin, Q., Liu, J. et al. Multipartite strongly symmetric states and applications to geometric entanglement and classicality. Quantum Inf Process 22, 291 (2023). https://doi.org/10.1007/s11128-023-04032-y

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