Consider a mixed quantum mechanical state, describing a statistical ensemble
in terms of an arbitrary density operator Ο of low purity, \tr\rho^2\ll
1, and yielding the ensemble averaged expectation value \tr(\rho A) for any
observable A. Assuming that the given statistical ensemble Ο is
generated by randomly sampling pure states β£Ο> according to the
corresponding so-called Gaussian adjusted projected measure [Goldstein et
al., J. Stat. Phys. 125, 1197 (2006)], the expectation value
is shown to be extremely close to the ensemble average \tr(\rho A) for the
overwhelming majority of pure states β£Ο> and any experimentally realistic
observable A. In particular, such a `typicality' property holds whenever the
Hilbert space \hr of the system contains a high dimensional subspace
\hr_+\subset\hr with the property that all |\psi>\in\hr_+ are realized with
equal probability and all other |\psi> \in\hr are excluded.Comment: accepted for publication in J. Stat. Phy