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
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 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 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.
Fund: 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).
Corresponding Authors:
Juan He, Liu Ye
E-mail: juanhe78@163.com;yeliu@ahu.edu.cn
Cite this article:
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 2022 Chin. Phys. B 31 060308
[1] Glauber R J 1963 Phys. Rev.130 2529 [2] Glauber R J 1963 Phys. Rev.131 2766 [3] Mandel L and Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press) [4] Chin A W, Prior J, Rosenbach R, Caycedo-Soler F, Huelga S F and Plenio M B 2013 Nat. Phys.9 113 [5] Ficek Z and Swain S 2005 Quantum Interference and Coherence: Theory and Experiments (New York: Springer) [6] Lostaglio M, Jennings D and Rudolph T 2015 Nat. Commun.6 6383 [7] Narasimhachar V and Gour G 2015 Nat. Commun.6 7689 [8] Lostaglio M, Korzekwa K, Jennings D and Rudolph T 2015 Phys. Rev. X5 021001 [9] Giovannetti V, Lloyd S and Maccone L 2006 Phys. Rev. Lett.96 010401 [10] Demkowicz-Dobrzański R and Maccone L 2014 Phys. Rev. Lett.113 250801 [11] Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photonics5 222 [12] Lambert N, Chen Y N, Cheng Y C, Li C M, Chen G Y and Nori F 2013 Nat. Phys.9 10 [13] Lloyd S 2011 J. Phys. Conf. Ser.302 012037 [14] Huelga S F and Plenio M B 2013 Contemp. Phys.54 181 [15] Svozilík J, Vallés A, Peřina J and Torres J P 2015 Phys. Rev. Lett.115 220501 [16] Kagalwala K H, Giuseppe G D, Abouraddy A F and Saleh B E 2013 Nat. Photonics7 72 [17] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett.113 140401 [18] Streltsov A, Adesso G and Plenio M B 2017 Rev. Mod. Phys.89 041003 [19] Hu M L, Hu X, Wang J C, Peng Y, Zhang Y R and Fan H 2018 Phys. Rep.762 1 [20] Winter A and Yang D 2016 Phys. Rev. Lett.116 120404 [21] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys.81 865 [22] Miranowicz A, Bartkiewicz K, Lambert N, Chen Y N and Nori F 2015 Phys. Rev. A92 062314 [23] Ge W, Tasgin M E and Zubairy M S 2015 Phys. Rev. A92 052328 [24] Cernoch A, Bartkiewicz K, Lemr K and Soubusta J 2018 Phys. Rev. A97 042305 [25] Nielsen M A and Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [26] Breuer H and Petruccione F 2002 The Theory of Open Quantum Systems (New York: Oxford University Press) [27] Zurek W H 2003 Rev. Mod. Phys.75 715 [28] Schlosshauer M 2005 Rev. Mod. Phys.76 1267 [29] Harouni M B 2021 Chin. Phys. B30 090301 [30] Luo Y and Li Y 2019 Chin. Phys. B28 040301 [31] Wu T and Song X K 2014 Chin. Phys. B23 100302 [32] Kimura G 2003 Phys. Lett. A314 339 [33] Gell-Mann M 1962 Phys. Rev.125 1067 [34] Zheng Y L, Zhen Y Z, Cao W F, Li L, Chen Z B, Liu N L and Chen K 2017 Phys. Rev. A95 032128 [35] Peng Y, Jiang Y and Fan H 2016 Phys. Rev. A93 032326 [36] Zhang H, Zhang C, Hu X M, Liu B H, Huang Y F, Li C F and Guo G C 2019 Phys. Rev. A99 052301 [37] Modi K, Brodutch A, Cable H, Paterek T and Vedral V 2012 Rev. Mod. Phys.84 1655 [38] Fan X G, Sun W Y, Ding Z Y, Ming F, Yang H, Wang D and Ye L 2019 New J. Phys.21 093053 [39] Mondal D, Pramanik T and Pati A K 2017 Phys. Rev. A95 010301 [40] Hu M L, Wang X M and Fan H 2018 Phys. Rev. A98 032317 [41] Ding Z Y, Yang H, Wang D, Yuan H, Yang J and Ye L 2019 Phys. Rev. A100 022308 [42] Chitambar E and Gour G 2019 Rev. Mod. Phys.91 025001
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
