Relative entropy in quantum information theory

We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to quantify quantum entanglement and analyze its manipulation. 1 Quantum relative entropy In this paper we discuss several uses of the quantum relative entropy function in quantum information theory. Relative entropy methods have a number of advantages. First of all, the relative entropy functional satisfies some strong identities and inequalities, providing a basis for good theorems. Secondly, the relative entropy has a natural interpretation in terms of the statistical distinguishability of quantum states; closely related to this is the picture of relative entropy as a “distance” measure between density operators. These interpretations of the relative entropy give insight about the meaning of the mathematical constructions that use it. Finally, relative entropy has found a wide variety of applications in quantum information theory.