-
Entanglement detection and classification of multipartite systems remain the key topics in the field of quantum information and science. In this work, we take advantage of the nature that quantum Fisher information (QFI) can witness multipartite entanglement to comprehensively investigate the entanglement detection and classification of multi-qubit $W\overline{W}$ states immersed in a white noise environment. In the situation of local operation, by combining the information of the known quantum state, we have presented a criterion with visibility for witnessing the genuine multipartite entanglement and another for identifying the presence of quantum entanglement. Specifically, with respect to the $5$-qubit $W\overline{W}$ state and $6$-qubit $W\overline{W}$ state, due to the fact that the maximum QFI of their splitting-structure states exceeds that of the original states, it is infeasible to strictly establish a criterion for detecting the genuine multipartite entanglement. However, we delineate the scope for inferring the possible entanglement structures. Furthermore, it is found that as the number of qubits increases, the conditions for witnessing the genuine multipartite entanglement become increasingly strict, while those for detecting the existence of entanglement grow relatively more relaxed. Taking into account the likelihood of the crosstalk between neighboring qubits during the local operations on the multipartite systems in experiments, we employ the Lipkin-Meshkov-Glick (LMG) model to explore the entanglement classification of diverse multi-qubit multipartite states. It is found that with the increasing interaction strength, even for the strong white noise, the $W\overline{W}$ states can still be distinguished, thereby resolving the challenge of managing the entanglement classification under local operation. Besides, as the interaction strength continues to increase, the task of entanglement classification becomes more straightforward. This fully shows the superiority of nonlocal operations over local operations in the aspect of entanglement classification.
-
Keywords:
- entanglement detection and classification /
- quantum Fisher information /
- multi-qubit $W\overline{W}$ state /
- white noise /
- Lipkin-Meshkov-Glick model
-
[1] Nielsen M A, Chuang I L Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000)
[2] Fan H 2018 Acta Phys. Sin. 67 060302 (in Chinese) [范桁 2018 物理学报 67 060302]
[3] Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367–374
[4] Athena K, Alasdair F, Gaetana S and Stefano P 2024 Rep. Prog. Phys. 87 094001
[5] Pezze L, Smerzi A, Oberthaler M K, Schmied R, and Treutlein P 2018 Rev. Mod. Phys. 90 035005
[6] Pezze L and Smerzi A 2020 Phys. Rev. Lett. 125 210503.
[7] Goel E O, Siegner U Quantum metrology: foundation of units and measurements, Wiley-VCH (2015)
[8] Guhne O, and Toth G 2009 Phys. Rep. 474 1
[9] Pezze L, Li Y, Li W D and Smerzi A 2016 Proc. Natl. Acad. Sci. 113 11459
[10] Lu H, 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, and Pan J W 2018 Phys. Rev. X 8 021072
[11] Ren Z H, Li W D, Smerzi A and Gessner M 2021 Phys. Rev. Lett. 126 080502
[12] Friis N, Vitagliano G, Malik M and Huber M 2019 Nat. Rev. Phys. 1 72
[13] Wineland D J, Bollinger J J, Itano W M, Moore F L and Heinzen D J 1992 Phys. Rev. A 46 R6797
[14] Strobel H, Muessel W, Linnemann D, Zibold T, Hume D B, Pezze L, Smerzi A, and Oberthaler M K 2014 Science 345 424
[15] Sperling J, Vogel W 2013 Phys. Rev. Lett. 111 110503
[16] Barreiro J T, Bancal J D, Schindler P, Nigg D, Hennrich M, Monz T, Gisin N and Blatt R 2013 Nat. Phys. 9 559
[17] Pezze L and Smerzi A 2009 Phys. Rev. Lett. 102 100401
[18] Hyllus P, Laskowski W, Krischek R, Schwemmer C, Wieczorek W, Weinfurter H, Pezze L and Smerzi A 2012 Phys. Rev. A 85 022321
[19] Das D, Dogra S, Dorai K and Arvind 2015 Phys. Rev. A 92 022307
[20] Sudha, Usha Devi A R and Rajagopal A K, 2012 Phys. Rev. A 85 012103
[21] Usha Devi A R, Sudha, Rajagopal A K, 2010 arXiv: 1002 2820
[22] Li Y, Ren Z H 2023 Phys. Rev. A 107 012403
[23] Ren Z H, Li Y 2023 Results in Physics 53 106954
[24] Zou Y Q, Wu L N, Liu Q, Luo X Y, Guo S F, Cao J H, Tey M K, You L 2018 Proc. Natl. Acad. Sci. 115 6381
[25] Manoj K J, Christian K, Rick v B, Florian K, Torsten V Z, Rainer B, Christian F R, Peter Z 2023 Nature 624 539
[26] Pratt J S and Eberly J H 2001 Phys. Rev. B 64 195314
[27] Parrado-Rodrguez P, Ryan-Anderson C, Bermudez A, and Muller M 2021 Quantum 5 487
[28] Li Y, Ren Z H 2022 Physica A 596 127137
[29] Lipkin H J, Meshkov N and Glick A 1965 Nucl. Phys. 62 188
[30] 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 040610]
[31] Huang J H, Zhuang M, and Lee C H 2024 Appl. Phys. Rev. 11 031302
[32] Holevo A S Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam (1982)
[33] Bohnet J G, Sawyer B C, Britton J W, Wall M L, Rey A M, Foss-Feig M, Bollinger J J 2016 Science 352 1297
[34] Hauke P, Heyl M, Tagliacozzo L, Zoller P 2016 Nat. Phys. 12 778
[35] Liu R, Wu Z, Li Y C, Chen Y Q, Peng X H 2023 Acta. Phys. Sin. 72 110305 (in Chinese) [刘然，吴泽，李宇晨，陈昱全，彭新华 2023 物理学报 72 110305]
[36] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
[37] Werner R F 1989 Phys. Rev. A 40 4277
[38] Wiesaw L, Tamas V and Marcin W 2015 J. Phys. A 48 465301
[39] Li Y and Li P F 2020 Phys. Lett. A 384 126413
[40] Dorner U 2012 New J. Phys. 14 043011
Metrics
- Abstract views: 134
- PDF Downloads: 1
- Cited By: 0
下载:
