Coherence migration in high-dimensional bipartite systems

doi:10.1088/1674-1056/ac48f8

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60308-060308.doi: 10.1088/1674-1056/ac48f8

Coherence migration in high-dimensional bipartite systems

Zhi-Yong Ding(丁智勇)^1,2, Pan-Feng Zhou(周攀峰)¹, Xiao-Gang Fan(范小刚)³, Cheng-Cheng Liu(刘程程)^1,2, Juan He(何娟)^1,2,†, and Liu Ye(叶柳)^3,‡

1 School of Physics and Electronic Engineering, Fuyang Normal University, Fuyang 236037, China;
2 Key Laboratory of Functional Materials and Devices for Informatics of Anhui Educational Institutions, Fuyang Normal University, Fuyang 236037, China;
3 School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230039, China

收稿日期:2021-09-15 修回日期:2021-12-28 接受日期:2022-01-07 出版日期:2022-05-17 发布日期:2022-05-17
通讯作者: Juan He, Liu Ye E-mail:juanhe78@163.com;yeliu@ahu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11605028), Anhui Provincial Natural Science Foundation, China (Grant Nos. 2108085MA18 and 2008085QA47), the Natural Science Research Project of Education Department of Anhui Province of China (Grant Nos. KJ2020A0527, KJ2021ZD0071 and KJ2021A0678), the Key Program of Excellent Youth Talent Project of the Education Department of Anhui Province of China (Grant No. gxyqZD2019042), and the Research Center for Quantum Information Technology of Fuyang Normal University (Grant No. kytd201706).

Coherence migration in high-dimensional bipartite systems

Zhi-Yong Ding(丁智勇)^1,2, Pan-Feng Zhou(周攀峰)¹, Xiao-Gang Fan(范小刚)³, Cheng-Cheng Liu(刘程程)^1,2, Juan He(何娟)^1,2,†, and Liu Ye(叶柳)^3,‡

1 School of Physics and Electronic Engineering, Fuyang Normal University, Fuyang 236037, China;
2 Key Laboratory of Functional Materials and Devices for Informatics of Anhui Educational Institutions, Fuyang Normal University, Fuyang 236037, China;
3 School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230039, China

Received:2021-09-15 Revised:2021-12-28 Accepted:2022-01-07 Online:2022-05-17 Published:2022-05-17
Contact: Juan He, Liu Ye E-mail:juanhe78@163.com;yeliu@ahu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11605028), Anhui Provincial Natural Science Foundation, China (Grant Nos. 2108085MA18 and 2008085QA47), the Natural Science Research Project of Education Department of Anhui Province of China (Grant Nos. KJ2020A0527, KJ2021ZD0071 and KJ2021A0678), the Key Program of Excellent Youth Talent Project of the Education Department of Anhui Province of China (Grant No. gxyqZD2019042), and the Research Center for Quantum Information Technology of Fuyang Normal University (Grant No. kytd201706).

摘要/Abstract

摘要： The conservation law for first-order coherence and mutual correlation of a bipartite qubit state was firstly proposed by Svozilík et al., and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary (m $\otimes$ n)-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, the coherence migration in open quantum systems is investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the (2 $\otimes$ 4)-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.

关键词: first-order coherence, mutual correlation, coherence migration, high-dimensional

Abstract: The conservation law for first-order coherence and mutual correlation of a bipartite qubit state was firstly proposed by Svozilík et al., and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary (m $\otimes$ n)-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, the coherence migration in open quantum systems is investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the (2 $\otimes$ 4)-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.

Key words: first-order coherence, mutual correlation, coherence migration, high-dimensional

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

03.67.-a (Quantum information) 34.80.Pa (Coherence and correlation)

Zhi-Yong Ding(丁智勇), Pan-Feng Zhou(周攀峰), Xiao-Gang Fan(范小刚),Cheng-Cheng Liu(刘程程), Juan He(何娟), and Liu Ye(叶柳). Coherence migration in high-dimensional bipartite systems[J]. 中国物理B, 2022, 31(6): 60308-060308.

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Coherence migration in high-dimensional bipartite systems

Coherence migration in high-dimensional bipartite systems

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