Entropy in Classical and Quantum Information Theory

Entropy is a central concept in both classical and quantum information theory, measuring the uncertainty and the information content in the state of a physical system. This paper reviews classical information theory and then proceeds to generalizations into quantum information theory. Both Shannon and Von Neumann entropy are discussed, making the connection to compressibility of a message stream and the generalization of compressibility in a quantum system. Finally, the paper considers the application of Von Neumann entropy in entanglement of formation for both pure and mixed bipartite quantum states.