The Quantum Computer - What Does It Means? - Kosiński, Janusz (Studia Informatica. System and information technology, 2007)
In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior to and independent of observation. Because of the completely different root of a quantum measurement as compared to a classical measurement, conceptual difficulties arise when we try to define the information gain in a quantum measurement using the notion of Shannon information. In contrast to classical measurements, quantum measurements, with very few exceptions, cannot be claimed to reveal a property of the individual quantum system existing before the measurement is performed. A mathematical theory of computation that is based on quantum physics is bound to be different. They are the analogues for quantum computers to classical logic gates for conventional digital computers. Although quantum gates work on qubits in a much different fashion from standard electronic circuits, they only differ in their basic effects in one sense: reversibility.