  Protective measurement, which was proposed as a method of observing the
wavefunction of a single system, is extended to the observation of the density
matrix of a single system. d'Espagnat's definition of `proper mixture' is shown
to be improper because it does not allow for appropriate fluctuations. His
claim that there could be different mixtures corresponding to the same density
matrix is critically examined. These results provide a new meaning to the
density matrix, which gives it the same ontological status as the wavefunction
describing a pure state. This also enables quantum entropy to be associated
with a single system.
