  We discuss reasons why a probability amplitude, which becomes a probability
density after squaring, is considered as one of the most basic ingredients of
quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of
motion in quantum mechanics, describes a time evolution of the probability
amplitude rather than of a probability density. There may be reasons why
dynamics of a physical system are described by amplitude. In order to
investigate one role of the probability amplitude in quantum mechanics,
specialized codeword-transfer experiments are designed using classical
information theory. Within this context, quantum mechanics based on probability
amplitude provides the following: i) a minimum error of the codeword transfer;
ii) this error is independent of coding parameters; and iii) nontrivial and
nonlocal correlation can be realized. These are considered essential advantages
of the probability amplitude over the probability density.
