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Entanglement detection and classification of different kinds of entangled states in quantum many-body systems have always been a key topic in quantum information and quantum computation. In this work, we investigate the entanglement detection and classification of three special entangled states: $4$-qubit GHZ state, $4$-qubit $W\overline{W}$ state, and $4$-qubit SGT state, which cannot be distinguished by the general quantum Fisher information (QFI) under the usual local operations. By utilizing the experimentally mature and controllable one-axis twisting model, accompanied by the optimized rotation and adjustable interaction strength, we successfully classify the three states by QFI. Besides, we have also studied the effects of four types of environmental noises on the entanglement detection, \textit{i.e.}, bit-flip channel, amplitude-damping channel, phase-damping channel, and depolarizing channel. The results show that under the local operation, the change of the QFI from the $4$-qubit GHZ state with respect to the decoherence parameter $p$ in four noise channels is significantly different from those from the $W\overline{W}$ state and SGT state, and it can be distinguished. However, the QFI from the $W\overline{W}$ state and the SGT state exhibit the same variations and cannot be classified. In the one-axis twisting model, the variation curves of the QFI from the three states under the four noise channels are mutually distinct and can be clearly observed. It should be noted that, in the bit-flip channel, the QFI of the $W\overline{W}$ state and the SGT state overlaps in the middle region ($p\approx0.5$), failing to be classified. Our work provides a new way to realize the entanglement detection and classification in quantum many-body systems, which will contribute to the future research in quantum science and technology.
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Keywords:
- entanglement detection and classification /
- quantum Fisher information /
- one-axis twisting model /
- GHZ state /
- $W\overline{W}$ state /
- SGT state
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[1] Gühne O, Tóth G 2009 Phys. Rep. 474 1
[2] Chefles A 2010 Contemporary Physics 41 401
[3] Bae J and Kwek L C 2015 J. Phys. A 48 083001
[4] Friis N, Vitagliano G, Malik M and Huber M 2019 Nat. Rev. Phys. 1 72
[5] Chen D X, Zhang Y, Zhao J L, Wu Q C, Fang Y L, Yang C P and Nori F 2022 Phys. Rev. A 106 022438
[6] Zhu C H, Shi T T, Ding L Y, Zheng Z Y, Zhang X, and Zhang W 2025 arXiv: 2502.20717v1
[7] Cramer M, Plenio M B, Flammia S T, Somma R, Gross D, Bartlett S D, Landon-Cardinal O, Poulin D, Liu Y K 2010 Nat. Commun. 1 149
[8] Wang T T, Song M H, Lyu L K, Witczak-Krempa W, Meng Z Y 2025 Nat. Commun. 16 96
[9] He L, Zhao Q, Li Z D, Yin X F, Yuan X, Hung J C, Chen L K, Li L, Liu N L, Peng C Z, Liang Y C, Ma X F, Chen Y A, Pan J W 2018 Phys. Rev. X 8 021072
[10] Zwerger, M, Dur, W, Bancal J D, Sekatski P 2019 Phys. Rev. Lett. 122 060502
[11] Pezze L and Smerzi A 2009 Phys. Rev. Lett. 102 100401
[12] Hyllus P, Laskowski W, Krischek R, Schwemmer C, Wieczorek W, Weinfurter H, Pezze L and Smerzi A 2012 Phys. Rev. A 85 022321
[13] Huang Y L, Che L Y, Wei C, Xu F, Nie X F, Li J, Lu D W, Xin T 2025 npj Quantum Inf. 11 29
[14] Ayachi F E, Mansour H A and Baz M E 2025 Commun. Theor. Phys. 77 065104
[15] Feng T F and Vedral V 2022 Phys. Rev. D 106 066013
[16] Li L J, Fan X G, Song X K, Ye L, and Wang D 2024 Phys. Rev. A 110 012418
[17] Qiu S F, Xu Q, Zhou X Q 2025 Acta Phys. Sin. 74 110301 (in Chinese) [丘尚锋, 徐桥, 周晓祺 2025 物理学报 74 110301]
[18] Li H, Gao T and Yan F L 2024 Phys. Rev. A 109 012213
[19] Dong D D, Li L J, Song X K, Ye L, and Wang D 2024 Phys. Rev. A 110 032420
[20] Strobel H, Muessel W, Linnemann D, Zibold T, Hume D B, Pezze L, Smerzi A, and Oberthaler M K 2014 Science 345 424
[21] Pezze L, Li Y, Li W D and Smerzi A 2016 Proc. Natl. Acad. Sci. 113 11459
[22] Pezze L, Smerzi A, Oberthaler M K, Schmied R, and Treutlein P 2018 Rev. Mod. Phys. 90 035005
[23] Ren Z H, Li Y, Li Y N, Li W D 2019 Acta. Phys. Sin. 68 040601 (in Chinese) [任志红，李岩，李艳娜，李卫东 2019 物理学报 68 040601]
[24] Qin Z Z, Gessner M, Ren Z H, Deng X W, Han D M, Li W D, Su X L, Smerzi A, Peng K C 2019 npj Quantum Inf. 5 3
[25] Ren Z H, Li W D, Smerzi A, Gessner M 2021 Phys. Rev. Lett. 126 080502
[26] Xu K, Zhang Y R, Sun Z H, Li H, Song P T, Xiang Z C, Huang K X, Li H, Shi Y H, Chen C T, Song X H, Zheng D N, Nori F, Wang H, Fan H 2022 Phys. Rev. Lett. 128 150501
[27] Li Y, Ren Z H 2023 Phys. Rev. A 107 012403
[28] Li Y, Ren Z H 2024 Chaos, Solitons and Fractals 186 115299
[29] Tey Meng-Khoon, You Li 2018 Acta Phys. Sin. 67 160303 (in Chinese) [郑盟锟, 尤力 2018 物理学报 67 160303]
[30] Fisher R A 1922 Philos. Trans. R. Soc. Lond. Ser. A 222 309
[31] Cramer H, Mathematical methods of statistics (Princeton University, Princeton, 1946)
[32] Li Y, Pezze L, Gessner M, Ren Z H, Li W D and Smerzi A 2018 Entropy 20 628
[33] Nolan S, Smerzi A and Pezze L 2021 npj Quantum Inf. 7 169
[34] Han C Y, Ma Z, Qiu Y X, Fang R H, Wu J T, Zhan C, Li M J, Huang J H, Lu B, Lee C H 2024 Phys. Rev. Applied 22 044058
[35] Li Y, Ren Z H 2022 Physica A 596 127137
[36] Imai S, Smerzi A, and Pezze L 2025 Phys. Rev. A 111 L020402
[37] Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439
[38] Shen Y, Zhou J G, Huang J H, Lee C H 2024 Phys. Rev. A 110 042619
[39] Fortes R and Rigolin G 2015 Phys. Rev. A 92 012338
[40] Kraus K, States, Effects and Operations: Fundamental Notions of Quantum Theory (Springer-Verlag, Berlin, 1983)
[41] Nielsen M A and Chuang I L, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000)
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