  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. The reason is
that, in contrast to classical measurement, quantum measurement, with very few
exceptions, cannot be claimed to reveal a property of the individual quantum
system existing before the measurement is performed.
