Quantum correlation measure based on min relative entropy for two-partition and k-partition

As a peculiar resource of quantum mechanics, quantum correlation has been applied in many aspects. In quantum information processing and quantum computing, quantum correlation plays an extremely important role, quantum correlation has been the subject of deep studies, principally due to the general belief that they are fundamental resources for different quantum information processing tasks. In addition, correlation measure is a very important physical quantity to study 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, by 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 proved that it satisfies some necessary properties of quantum correlation measures, including: the nonnegativity, the invariance under local unitary operators, and monotonicity under completely positive trace-preserving. By proving these properties, we show that the given correlation measure is well-defined. Communication security has been paid attention to by people since ancient times. In today's society, with the continuous improvement of the degree of information, such as the internet, instant messaging and e-commerce applications are related to information security, and information security is related to the vital interests of everyone. Information encryption is one of the important methods to ensure information security. As an important way to ensure information security, quantum channel has been paid 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.