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在量子信息领域, 不同纠缠态的判定与分类一直以来就是人们所关注的重点课题. 本文借助实验上成熟可控的单轴旋转模型, 对常规局域操作下无法利用量子Fisher信息实现区分的三种特殊纠缠态(4比特GHZ态, 4比特$W\overline{W}$态, 4比特SGT态)开展纠缠判定研究. 通过对三种量子态在单轴旋转模型下进行方向优化和 相互作用强度调节, 实现了三者的量子Fisher信息区分. 另外, 我们还研究了四种环境噪声(即比特翻转信道, 振幅阻尼信道, 相位阻尼信道, 去极化信道)对纠缠判定的影响. 结果显示, 在局域操作下, 4比特GHZ态的量子Fisher信息在四种噪声通道中随退相干参数p的变化明显区别于$W\overline{W}$态和SGT态, 可以区分, 而$W\overline{W}$态和SGT态的 量子Fisher信息变化相同, 无法区分. 在单轴旋转模型下, 三种量子态的量子Fisher信息在四种噪声通道下的变化曲线互不相同, 可以明显区分. 需要注意的是, 在比特翻转通道中, 随着退相干参数p的变化, $W\overline{W}$态与SGT态的量子Fisher信息在中间区域($p \sim0.5$)有重叠, 无法区分. 我们的工作为多体系统的量子纠缠判定提供了一种新的思路, 将有助于量子信息技术的进一步发展.
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关键词:
- 纠缠判定与分类 /
- 量子Fisher信息 /
- 单轴旋转模型 /
- GHZ态 /
- $W\overline{W} $态 /
- SGT态
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, 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.-
Keywords:
- entanglement detection and classification /
- quantum Fisher information /
- one-axis twisting model /
- GHZ state /
- $W\overline{W} $ state /
- SGT state
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图 1 (color online) 4量子比特GHZ态、$ W\overline{W} $态和SGT态在单轴旋转模型下的量子Fisher信息. 黑色圆点, 蓝色三角形, 红色方块依次表示GHZ态, $ W\overline{W} $态和SGT态的量子Fisher信息随相互作用参数γ的变化结果. 其中, (a)表示彼此独立优化旋转方向n下的结果, 算式(25); (b)表示单轴旋转为x轴的结果, 算式(26); (c)表示单轴旋转为y轴的结果, 算式(27); (d)单轴旋转为z轴的结果, 算式(29)
Fig. 1. The QFI of the 4-qubit GHZ state, $ W\overline{W} $ state and SGT state under the one-axis twisting model. Black dots, blue triangles and red squares represent the QFI of the GHZ state, $ W\overline{W} $, and SGT state with respect to the interaction parameter γ. (a) shows the results under the condition that the rotation directions n are optimized independently, Eq. (25); (b) shows the results when the rotation is along the x-axis, Eq. (26); (c) shows the results when the rotation is along the y-axis, Eq. (27); (d) shows the results when the rotation is along the z-axis, Eq. (29).
图 2 (color online) 在局域操作下, 4量子比特GHZ态、$ W\overline{W} $态和SGT态在比特翻转, 相位阻尼, 振幅阻尼和去极化通道下的量子Fisher信息. 黑色圆点, 蓝色三角形, 红色方块依次表示GHZ态, $ W\overline{W} $态和SGT态的量子Fisher信息随退相干参数p的变化结果. 其中, (a)表示量子态在比特翻转通道下的结果; (b)表示量子态在相位阻尼通道中的结果; (c)表示在振幅阻尼通道中的结果; (d)表示在去极化通道下的结果
Fig. 2. The QFI of the 4-qubit GHZ state, $ W\overline{W} $ state and SGT state under the bit-flip, phase damping, amplitude damping, and depolarizing channels with local operations. Black dots, blue triangles and red squares represent the QFI of the GHZ state, $ W\overline{W} $, and SGT state with respect to the decoherence parameter p. (a) shows the results under the bit-flip channel; (b) shows the results under the phase damping channel; (c) shows the results under the amplitude damping channel; (d) shows the results under the depolarizing channel.
图 3 (color online) 在单轴旋转模型下($ \gamma=2 $), 4量子比特GHZ态、$ W\overline{W} $态和SGT态在比特翻转, 相位阻尼, 振幅阻尼和去极化通道下的量子Fisher信息. 黑色圆点, 蓝色三角形, 红色方块依次表示GHZ态, $ W\overline{W} $态和SGT态的量子Fisher信息随退相干参数p的变化结果. 其中, (a)表示量子态在比特翻转通道下的结果; (b)表示量子态在相位阻尼通道中的结果; (c)表示在振幅阻尼通道中的结果; (d)表示在去极化通道下的结果
Fig. 3. The QFI of the 4-qubit GHZ state, $ W\overline{W} $ state and SGT state under the bit-flip, phase damping, amplitude damping, and depolarizing channels in the one-axis twisting model ($ \gamma=2 $). Black dots, blue triangles and red squares represent the QFI of the GHZ state, $ W\overline{W} $, and SGT state with respect to the decoherence parameter p. (a) shows the results under the bit-flip channel; (b) shows the results under the phase damping channel; (c) shows the results under the amplitude damping channel; (d) shows the results under the depolarizing channel.
图 4 (color online) 在单轴旋转模型下($ \gamma=5 $), 4量子比特GHZ态、$ W\overline{W} $态和SGT态在比特翻转, 相位阻尼, 振幅阻尼和去极化通道下的量子Fisher信息. 黑色圆点, 蓝色三角形, 红色方块依次表示GHZ态, $ W\overline{W} $态和SGT态的量子Fisher信息随退相干参数p的变化结果. 其中, (a)表示量子态在比特翻转通道下的结果; (b)表示量子态在相位阻尼通道中的结果; (c)表示在振幅阻尼通道中的结果; (d)表示在去极化通道下的结果
Fig. 4. The QFI of the 4-qubit GHZ state, $ W\overline{W} $ state and SGT state under the bit-flip, phase damping, amplitude damping, and depolarizing channels in the one-axis twisting model ($ \gamma=5 $). Black dots, blue triangles and red squares represent the QFI of the GHZ state, $ W\overline{W} $, and SGT state with respect to the decoherence parameter p. (a) shows the results under the bit-flip channel; (b) shows the results under the phase damping channel; (c) shows the results under the amplitude damping channel; (d) shows the results under the depolarizing channel.
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