Quantum Information Theory and Applications to Quantum Cryptography

Abstract

Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate why the density matrix is the main tool of quantum information theory. Then von Neumann entropy is introduced and with its help a great difference between classical and quantum information theory is presented: quantum entanglement. Moreover an information theoretic interpretation of quantum measurement is discussed. Data compression, error correction and noisy channel transmission are simply demonstrated for both classical and quantum cases. Finally using the above theory quantum cryptography is reviewed and the possibility of a commercial device realizing it is explored.