Quantum speed limit for mixed states in a unitary system

doi:10.1088/1674-1056/ac76b4

中国物理B ›› 2022, Vol. 31 ›› Issue (11): 110307-110307.doi: 10.1088/1674-1056/ac76b4

Quantum speed limit for mixed states in a unitary system

Jie-Hui Huang(黄接辉)^1,2,†, Li-Guo Qin(秦立国)¹, Guang-Long Chen(陈光龙)¹, Li-Yun Hu(胡利云)^2,‡, and Fu-Yao Liu(刘福窑)^1,§

1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2 College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2022-01-23 修回日期:2022-05-17 接受日期:2022-06-08 出版日期:2022-10-17 发布日期:2022-10-19
通讯作者: Jie-Hui Huang, Li-Yun Hu, Fu-Yao Liu E-mail:huangjh@sues.edu.cn;hlyun@jxnu.edu.cn;liu-fuyao@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11664018, 12174247, and U2031145).

Quantum speed limit for mixed states in a unitary system

Jie-Hui Huang(黄接辉)^1,2,†, Li-Guo Qin(秦立国)¹, Guang-Long Chen(陈光龙)¹, Li-Yun Hu(胡利云)^2,‡, and Fu-Yao Liu(刘福窑)^1,§

1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2 College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China

Received:2022-01-23 Revised:2022-05-17 Accepted:2022-06-08 Online:2022-10-17 Published:2022-10-19
Contact: Jie-Hui Huang, Li-Yun Hu, Fu-Yao Liu E-mail:huangjh@sues.edu.cn;hlyun@jxnu.edu.cn;liu-fuyao@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11664018, 12174247, and U2031145).

摘要/Abstract

摘要： Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it, we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit (QSL) of a mixed state. We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system, which automatically reduces to the quantum speed limit induced by the Fubini-Study metric for pure states. The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state, where we have to make a singular value decomposition (SVD) on the inner product between the two eigenvector matrices of the initial and target states. By combing these results, a lower bound for the evolution time of a general mixed state is presented. In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references, two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically, respectively. All conclusions derived in this work are independent of the eigenvalues of the mixed state, which is in accord with the evolution properties of a quantum unitary system.

关键词: quantum speed limit, instantaneous angular velocity, singular value decomposition

Abstract: Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it, we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit (QSL) of a mixed state. We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system, which automatically reduces to the quantum speed limit induced by the Fubini-Study metric for pure states. The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state, where we have to make a singular value decomposition (SVD) on the inner product between the two eigenvector matrices of the initial and target states. By combing these results, a lower bound for the evolution time of a general mixed state is presented. In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references, two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically, respectively. All conclusions derived in this work are independent of the eigenvalues of the mixed state, which is in accord with the evolution properties of a quantum unitary system.

Key words: quantum speed limit, instantaneous angular velocity, singular value decomposition

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Fd (Algebraic methods) 03.65.Ta (Foundations of quantum mechanics; measurement theory)

Jie-Hui Huang(黄接辉), Li-Guo Qin(秦立国), Guang-Long Chen(陈光龙), Li-Yun Hu(胡利云), and Fu-Yao Liu(刘福窑). Quantum speed limit for mixed states in a unitary system[J]. 中国物理B, 2022, 31(11): 110307-110307.

Jie-Hui Huang(黄接辉), Li-Guo Qin(秦立国), Guang-Long Chen(陈光龙), Li-Yun Hu(胡利云), and Fu-Yao Liu(刘福窑). Quantum speed limit for mixed states in a unitary system[J]. Chin. Phys. B, 2022, 31(11): 110307-110307.

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Quantum speed limit for mixed states in a unitary system

Quantum speed limit for mixed states in a unitary system

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