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As a peculiar resource of quantum mechanics, quantum correlation has been applied to many aspects. In quantum information processing and quantum computing, the quantum correlation plays an extremely important role, and it has been a subject of further studies, principally due to the general belief that it is a fundamental resource for different quantum information processing tasks. In addition, correlation measure is a very important physical quantity in studying the quantum correlation. A well-defined correlation measure needs to have some necessary properties. By proving these necessary properties, we can deepen our understanding of correlation measure. As one of the key concepts of quantum information theory, relative entropy is always used to measure the uncertainty contained in the state of physical system. In order to better understand the properties and applications of correlation measure based on relative entropy, in this paper, according to the properties of the min relative entropy, we give the quantum correlation measure based on min relative entropy for two-partition and k-partition. Furthermore, we prove that it satisfies some necessary properties of quantum correlation measures, including the nonnegativity, the invariance under local unitary operators, and the monotonicity under completely positive trace-preserving. By proving these properties, we show that the given correlation measure is well-defined. Security of communication has received much attention since ancient times. In today's society, the internet, instant messaging and e-commerce applications are all related to the information security, and the information security is related to the vital interests of everyone. The information encryption is one of the important methods to ensure information security. As an important way to ensure information security, quantum channel has received more and more attention. At the end of the paper, we introduce the concept of quantum channel, and discuss the influence of quantum channel on the correlation measure based on min relative entropy under k-partition. By proposing a new correlation measure and proving the effect quantum channel on the measure, we can better describe the uncertainty contained in the state of physical system.
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Keywords:
- correlation measure /
- relative entropy /
- k-partition /
- trace mapping /
- quantum systems
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[1] Goh K T, Kaniewski J, Wolfe E 2018 Phys. Rev. A 97 022104
Google Scholar
[2] Rundle R, Everitt M J 2021 J. Comput. Electron. 20 2180
Google Scholar
[3] Qars J E 2021 Commun. Theor. Phys. 73 176
Google Scholar
[4] 董曜, 纪爱玲, 张国锋 2022 物理学报 71 070303
Google Scholar
Dong Y, Ji A L, Zhang G F 2022 Acta. Phys. Sin. 71 070303
Google Scholar
[5] Benrass N, Aoune D, Habiballah N 2022 Mod. Phys. Lett. A 37 406
Google Scholar
[6] 曹雷明, 杜金鉴, 张凯 2022 物理学报 71 160306
Google Scholar
Cao L M, Du J J, Zhang K 2022 Acta. Phys. Sin. 71 160306
Google Scholar
[7] Yang Y Y, Li L J, Ye L 2022 Chin. Phys. B 31 100303
Google Scholar
[8] Tiokang O M, Tchangnwa F N, Tchinda J D 2022 Chin. Phys. B 31 110305
Google Scholar
[9] Sarkar P J 2020 Pure. Appl. Algebra. 224 789
Google Scholar
[10] Chen K, Wu L G 2002 Quantum. Inf. Comput. 3 193
Google Scholar
[11] Anstock F, Schorbach V A 2020 J. Phys. Conf. Ser. 1618 022062
Google Scholar
[12] Lewenstein M, Kraus B, Cirac J I 2000 Phys. Rev. A 62 2310
Google Scholar
[13] Gao X H, Albeverio S, Chen K 2008 Front. Comput. Sci. Chi. 2 114
Google Scholar
[14] Bordbar M, Naderi N, Chamgordani M A 2020 India. J. Phys. 2 901
Google Scholar
[15] Duan Z B, Niu L F, Wang Y Y 2017 Int. J. Theor. Phys. 56 1929
Google Scholar
[16] Oliveria A D, Buksman E, Lacalle J D 2014 Int. J. Mod. Phys. B 28 1450050
Google Scholar
[17] Baba H, Mansour M, Daoud M 2022 J. Russ. Laser. Res. 43 124
Google Scholar
[18] Sumiyoshi, ABE 2003 Phys. Rev. A 312 336
Google Scholar
[19] Datta N 2009 Ieee. T. Inform. Theory. 55 2816
Google Scholar
[20] Wang Y Z, Hou J C 2015 Quantum. Inf. Process. 14 3711
Google Scholar
[21] Liu J, Jing X Q, Zhong W 2014 Commun. Theor. Phys. 61 45
Google Scholar
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