As a peculiar resource of quantum mechanics, quantum correlation has been applied to many aspects. Inquantum information processing and quantum computing, the quantum correlation plays an extremelyimportant role, and it has been a subject of further studies, principally due to the general belief that it is afundamental resource for different quantum information processing tasks. In addition, correlation measure is avery important physical quantity in studying the quantum correlation. A well-defined correlation measure needsto have some necessary properties. By proving these necessary properties, we can deepen our understanding ofcorrelation measure. As one of the key concepts of quantum information theory, relative entropy is always usedto measure the uncertainty contained in the state of physical system. In order to better understand theproperties and applications of correlation measure based on relative entropy, in this paper, according to theproperties of the min relative entropy, we give the quantum correlation measure based on min relative entropyfor two-partition and k-partition. Furthermore, we prove that it satisfies some necessary properties of quantumcorrelation measures, including the nonnegativity, the invariance under local unitary operators, and themonotonicity under completely positive trace-preserving. By proving these properties, we show that the givencorrelation 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 theinformation security, and the information security is related to the vital interests of everyone. The informationencryption is one of the important methods to ensure information security. As an important way to ensureinformation security, quantum channel has received more and more attention. At the end of the paper, weintroduce the concept of quantum channel, and discuss the influence of quantum channel on the correlationmeasure based on min relative entropy under k-partition. By proposing a new correlation measure and provingthe effect quantum channel on the measure, we can better describe the uncertainty contained in the state of physical system
