CHAPTER 3 - Classical and Quantum Information Theory

Abstract

The properties of classical and quantum information are very different. Classical information is carried by systems with a definite state, and it can be replicated and measured without being altered. Quantum information is encoded as a property of quantum systems (e.g., photon polarization or particle and has special properties such as superposition and entanglement with no classical counterpart; quantum information cannot be cloned, and it is altered as a result of a measurement. This chapter discusses the physical support of information and overviews several properties of classical information based on Shannon's theory, concentrating on the properties of quantum information, sources and, quantum channels. The Landauer principle relates information with thermodynamic entropy. Once the thermodynamic effect of information erasure is established, the physical nature of information can be quantified. The amount of information that can be stored or transmitted by a physical system is related to the number of states the system. The entropy, an important concept in thermodynamics, Shannon's information theory, as well as quantum information theory, is a function of the logarithm of the number of states of a system; this logarithm is equal to the number of bits required to uniquely identify the state of the system—in other words, to label a state. The label becomes an element of the state and any state transformation will affect the label; to prepare a system in a certain state, the label of the previous state has to be erased. Shannon entropy is used to characterize a source of classical information as well as the properties of a classical communication channel.