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多体系统的纠缠判定与分类是当前量子信息领域人们研究的重点课题. 本文利用量子Fisher信息(quantum Fisher information, QFI)可以判定多体纠缠这一特性, 对多量子比特WW态在白噪声环境下的量子纠缠进行了判定与分类研究. 在局域操作下, 结合已知量子态的信息, 我们给出了判定真正多体纠缠和含有量子纠缠的可见度判据.特别地, 对于5比特WW态和6比特WW态, 由于其拆分结构态的QFI最大值大于其本身的QFI, 所以无法严格地给出判定其真正多体纠缠的判据, 但给出了判定其可能是哪种纠缠结构的范围. 另外, 研究还发现随着量子比特数目的增加, 判定WW态真正多体纠缠的条件变得越来越严苛, 而判定其含有纠缠的条件变得相对宽松. 考虑实验上对多体系统进行局域操作时, 紧邻量子比特间容易发生串扰现象, 我们借助Lipkin-Meshkov-Glick模型对不同多量子比特WW态的纠缠分类进行了研究, 发现随着相互作用强度的增加, 即使在白噪声占比较大的情况下,不同量子比特数的WW态也可以区分, 解决了局域操作下区分困难的问题, 且随着相互作用强度的增大, 纠缠分类越容易实现. 这一点也充分展现了非局域操作相较于局域操作在纠缠分类方面的优势.
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关键词:
- 纠缠判定与分类 /
- 量子Fisher信息 /
- 多量子比特态 /
- 白噪声 /
- Lipkin-Meshkov-Glick模型
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 WW 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 WW state and 6-qubit WW 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 WW 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 state /
- white noise /
- Lipkin-Meshkov-Glick model
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图 1 在局域操作下, 判定含白噪声的多量子比特$ W{\overline{W}} $态是真正多体纠缠的判据与含有纠缠的判据随粒子数目$ N $的变化情况. 红色圆点代表真正多体纠缠的可见度判据, 其中, $ 5, 6 $量子比特属于特殊情况, 用空心圆点表示, 其无法确定真正多体纠缠判定, 但缩小了可能的范围, 详见文中叙述. 蓝色实心圆点代表含有纠缠的可见度判据
Fig. 1. The criteria for witnessing genuine multipartite entanglement and the presence of entanglement with respect to the number of qubits under local operations for multi-qubit $ W{\overline{W}} $ states in the white noise environment. Red solid dots represent the visibility criterion for genuine multipartite entanglement. The $ 5 $-qubit case and $ 6 $-qubit case are the special ones and represented by hollow red dots. For the both, it is impossible to witness the genuine multipartite entanglement, but the possible scope has been narrowed down, and the details can be found in the main context. Blue solid dots represent the visibility criterion for the presence of entanglement.
图 2 (a) 不同颜色的实线(绿色到蓝色)从下到上依次表示$ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10 $量子比特$ W{\overline{W}} $态的量子Fisher信息$ F_{\rm{lmg}}^{(N)} $在无噪声情况下随相互作用强度$ \gamma $的变化情况; (b) 蓝色实心圆点表示转折点$ \gamma_t^{(N)} $随粒子数目$ N $的变化情况, 红色实线代表$ \gamma_t \simeq \dfrac{1}{\sqrt{3 N}} $
Fig. 2. (a) The colorful solid lines (from green to blue) respectively represent the variations of the QFI of the $ W{\overline{W}} $ state with $ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10 $ qubits, with respect to the interaction strength $ \gamma $ in the absence of noise. (b) The blue dots represent the variation of the turning point $ \gamma_t^{(N)} $ with respect to the number of qubits, and the red line represents $ \gamma_t \simeq \dfrac{1}{\sqrt{3 N}} $.
图 3 (a), (b), (c), (d)分别表示多量子比特$ W{\overline{W}} $态在噪声环境$ V=0.1,\ 0.3,\ 0.6,\ 0.9 $下的量子Fisher信息随相互作用强度$ \gamma $的变化. 以(d)为例, 不同颜色的实线(绿色到蓝色)从下到上依次代表$ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10 $量子比特$ W{\overline{W}} $态的QFI的变化情况
Fig. 3. (a), (b), (c), (d) respectively show the quantum Fisher information of an $ N $-qubit $ W{\overline{W}} $ state with respect to $ \gamma $ under the white noise situation $ V=0.1,\ 0.3,\ 0.6,\ 0.9 $. Taking Fig. (d) as an example, the colorful solid lines (green to blue) from bottom to top respectively denote the variation trends of QFI from $ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10 $-qubit $ W{\overline{W}} $ state.
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