Information content for quantum states

A method for representing probabilistic aspects of quantum systems by means of a density function on the space of pure quantum states is introduced. I n particular, a maximum entropy argument allows us to obtain a natural dens ity function that only reflects the information provided by the density mat rix. This result is applied to derive the Shannon entropy of a quantum stat e. The information theoretic quantum entropy thereby obtained is shown to h ave the desired concavity property, and to differ from the conventional von Neumann entropy. This is illustrated explicitly for a two-state system. (C ) 2000 American Institute of Physics. [S0022-2488(00)03305-3].